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Volumn 1, Issue 1, 2012, Pages

The Kardar-Parisi-Zhang Equation and Universality Class

Author keywords

anomalous fluctuations; asymmetric exclusion process; directed polymers; Kardar Parisi Zhang equation; random growth; stochastic Burgers equation; stochastic heat equation

Indexed keywords


EID: 85043627068     PISSN: 20103263     EISSN: 20103271     Source Type: Journal    
DOI: 10.1142/S2010326311300014     Document Type: Article
Times cited : (866)

References (170)
  • 1
    • 23244433542 scopus 로고    scopus 로고
    • PDEs for the joint distributions of the Dyson, Airy and Sine processes
    • M. Adler and P. van Moerbeke, PDEs for the joint distributions of the Dyson, Airy and Sine processes, Ann. Probab. 33 (2005) 1326-1361.
    • (2005) Ann Probab. , vol.33 , pp. 1326-1361
    • Adler, M.1    Van Moerbeke, P.2
  • 2
    • 77955943258 scopus 로고    scopus 로고
    • The intermediate disorder regime for directed polymers in dimension 1 + 1
    • T. Alberts, K. Khanin and J. Quastel, The intermediate disorder regime for directed polymers in dimension 1 + 1, Phys. Rev. Lett. 105 (2010) 090603.
    • (2010) Phys. Rev. Lett. , vol.105 , pp. 090603
    • Alberts, T.1    Khanin, K.2    Quastel, J.3
  • 3
    • 0033458290 scopus 로고    scopus 로고
    • Longest increasing subsequences: From patience sorting to the Baik-Deift-Johansson theorem
    • D. Aldous and P. Diaconis, Longest increasing subsequences: From patience sorting to the Baik-Deift-Johansson theorem, Bull. Amer. Math. Soc. 36 (1999) 413-432.
    • (1999) Bull. Amer. Math. Soc. , vol.36 , pp. 413-432
    • Aldous, D.1    Diaconis, P.2
  • 4
    • 33746902440 scopus 로고    scopus 로고
    • Pinning of polymers and interfaces by random potentials
    • K. S. Alexander and V. Sidoravicius, Pinning of polymers and interfaces by random potentials, Ann. Appl. Probab. 16 (2006) 636-669.
    • (2006) Ann. Appl. Probab. , vol.16 , pp. 636-669
    • Alexander, K.S.1    Sidoravicius, V.2
  • 5
    • 78650327767 scopus 로고    scopus 로고
    • Probability distribution of the free energy of the continuum directed random polymer in 1+1 dimensions
    • G. Amir, I. Corwin and J. Quastel, Probability distribution of the free energy of the continuum directed random polymer in 1+1 dimensions, Commun. Pure Appl. Math. 64 (2011) 466-537.
    • (2011) Commun. Pure Appl. Math. , vol.64 , pp. 466-537
    • Amir, G.1    Corwin, I.2    Quastel, J.3
  • 6
    • 33745806602 scopus 로고    scopus 로고
    • Analysis of airplane boarding via space-time geometry and random matrix theory
    • E. Bachmat, D. Berend, L. Sapir, S. Skiena and N. Stolyarov, Analysis of airplane boarding via space-time geometry and random matrix theory, J. Phys. A 39 (2006) 453-459.
    • (2006) J. Phys. A , vol.39 , pp. 453-459
    • Bachmat, E.1    Berend, D.2    Sapir, L.3    Skiena, S.4    Stolyarov, N.5
  • 7
    • 84968520048 scopus 로고
    • Natural sorting over permutation spaces
    • R. M. Baer and P. Brock, Natural sorting over permutation spaces, Math. Comp. 22 (1968) 385-410.
    • (1968) Math. Comp. , vol.22 , pp. 385-410
    • Baer, R.M.1    Brock, P.2
  • 8
    • 27644476898 scopus 로고    scopus 로고
    • Phase transition of the largest eigenvalue for non-null complex sample covariance matrices
    • J. Baik, G. Ben Arous and S. Peché, Phase transition of the largest eigenvalue for non-null complex sample covariance matrices, Ann. Probab. 33 (2006) 1643-1697.
    • (2006) Ann. Probab. , vol.33 , pp. 1643-1697
    • Baik, J.1    Ben Arous, G.2    Peche, S.3
  • 9
    • 0033443150 scopus 로고    scopus 로고
    • On the distribution of the length of the longest increasing subsequence of random permutations
    • J. Baik, P. A. Deift and K. Johansson, On the distribution of the length of the longest increasing subsequence of random permutations, J. Amer. Math. Soc. 12 (1999) 1119-1178.
    • (1999) J. Amer. Math. Soc. , vol.12 , pp. 1119-1178
    • Baik, J.1    Deift, P.A.2    Johansson, K.3
  • 10
    • 77954028328 scopus 로고    scopus 로고
    • Limit process of stationary TASEP near the characteristic line
    • J. Baik, P. L. Ferrari and S. Peché, Limit process of stationary TASEP near the characteristic line, Commun. Pure Appl. Math. 63 (2010) 1017-1070.
    • (2010) Commun. Pure Appl. Math. , vol.63 , pp. 1017-1070
    • Baik, J.1    Ferrari, P.L.2    Peché, S.3
  • 11
    • 0034338413 scopus 로고    scopus 로고
    • Limiting distributions for a polynuclear growth model with external sources
    • J. Baik and E. Rains, Limiting distributions for a polynuclear growth model with external sources, J. Stat. Phys. 100 (2000) 523-542.
    • (2000) J. Stat. Phys. , vol.100 , pp. 523-542
    • Baik, J.1    Rains, E.2
  • 12
    • 0010151103 scopus 로고    scopus 로고
    • The asymptotics of monotone subsequences of involutions
    • J. Baik and E. Rains, The asymptotics of monotone subsequences of involutions, Duke Math. J. 109 (2001) 205-281.
    • (2001) Duke Math. J. , vol.109 , pp. 205-281
    • Baik, J.1    Rains, E.2
  • 13
    • 0010126887 scopus 로고    scopus 로고
    • Symmetrized random permutations
    • eds. P. Bleher and A. Its, MSRI
    • J. Baik and E. Rains, Symmetrized random permutations, in Random Matrix Models and Their Applications, eds. P. Bleher and A. Its, MSRI Vol. 40 (2001), pp. 1-19.
    • (2001) Random Matrix Models and Their Applications , vol.40 , pp. 1-19
    • Baik, J.1    Rains, E.2
  • 15
    • 70349691826 scopus 로고    scopus 로고
    • Fluctuation bounds for the asymmetric simple exclusion process
    • M. Balázs and T. Seppälaïnen, Fluctuation bounds for the asymmetric simple exclusion process, ALEA 6 (2009) 1-24.
    • (2009) ALEA , vol.6 , pp. 1-24
    • Balázs, M.1    Seppälaïnen, T.2
  • 17
    • 78650289779 scopus 로고    scopus 로고
    • Current fluctuations for TASEP: A proof of the Prähofer-Spohn conjecture
    • G. Ben Arous and I. Corwin, Current fluctuations for TASEP: A proof of the Prähofer-Spohn conjecture, Ann. Probab. 39 (2011) 104-138.
    • (2011) Ann. Probab. , vol.39 , pp. 104-138
    • Ben Arous, G.1    Corwin, I.2
  • 18
    • 0001542406 scopus 로고
    • Excess noise for driven diffusive systems
    • H. van Beijeren, R. Kutner and H. Spohn, Excess noise for driven diffusive systems, Phys. Rev. Lett. 54 (1985) 2026-2029.
    • (1985) Phys. Rev. Lett. , vol.54 , pp. 2026-2029
    • Van Beijeren, H.1    Kutner, R.2    Spohn, H.3
  • 19
    • 0346962333 scopus 로고    scopus 로고
    • First passage percolation has sublinear distance variance
    • I. Benjamini, G. Kalai and O. Schramm, First passage percolation has sublinear distance variance, Ann. Probab. 31 (2003) 1970-1978.
    • (2003) Ann. Probab. , vol.31 , pp. 1970-1978
    • Benjamini, I.1    Kalai, G.2    Schramm, O.3
  • 20
    • 21844507768 scopus 로고
    • The stochastic heat equation: Feynman-Kac formula and intermittence
    • L. Bertini and N. Cancrini, The stochastic heat equation: Feynman-Kac formula and intermittence, J. Stat. Phys. 78 (1995) 1377-1401.
    • (1995) J. Stat. Phys. , vol.78 , pp. 1377-1401
    • Bertini, L.1    Cancrini, N.2
  • 21
    • 0031065063 scopus 로고    scopus 로고
    • Stochastic Burgers and KPZ equations from particle systems
    • L. Bertini and G. Giacomin, Stochastic Burgers and KPZ equations from particle systems, Commun. Math. Phys. 183 (1997) 571-607.
    • (1997) Commun. Math. Phys. , vol.183 , pp. 571-607
    • Bertini, L.1    Giacomin, G.2
  • 24
    • 0001397647 scopus 로고
    • A note on diffusion of directed polymers in a random environment
    • E. Bolthausen, A note on diffusion of directed polymers in a random environment, Commun. Math. Phys. 123 (1989) 529-534.
    • (1989) Commun. Math. Phys. , vol.123 , pp. 529-534
    • Bolthausen, E.1
  • 25
    • 77953533177 scopus 로고    scopus 로고
    • On the numerical evaluation of Fredholm determinants
    • F. Bornemann, On the numerical evaluation of Fredholm determinants, Math. Comp. 79 (2010) 871-915.
    • (2010) Math. Comp. , vol.79 , pp. 871-915
    • Bornemann, F.1
  • 27
    • 50249139589 scopus 로고    scopus 로고
    • Large time asymptotics of growth models on space-like paths I: PushASEP
    • A. Borodin and P. L. Ferrari, Large time asymptotics of growth models on space-like paths I: PushASEP, Electron. J. Probab. 13 (2008) 1380-1418.
    • (2008) Electron J. Probab. , vol.13 , pp. 1380-1418
    • Borodin, A.1    Ferrari, P.L.2
  • 29
    • 36448967090 scopus 로고    scopus 로고
    • Fluctuation properties of the TASEP with periodic initial configuration
    • A. Borodin, P. L. Ferrari, M. Prähofer and T. Sasamoto, Fluctuation properties of the TASEP with periodic initial configuration, J. Stat. Phys. 129 (2007) 1055-1080.
    • (2007) J. Stat. Phys. , vol.129 , pp. 1055-1080
    • Borodin, A.1    Ferrari, P.L.2    Prähofer, M.3    Sasamoto, T.4
  • 30
    • 36448953578 scopus 로고    scopus 로고
    • Fluctuations in the discrete TASEP with periodic initial configurations and the Airy1 process
    • A. Borodin, P. L. Ferrari, M. Prähofer and T. Sasamoto, Fluctuations in the discrete TASEP with periodic initial configurations and the Airy1 process, Int. Math. Res. Papers, 2007:rpm002 (2007).
    • (2007) Int. Math. Res. Papers , vol.2007 , pp. 2
    • Borodin, A.1    Ferrari, P.L.2    Prähofer, M.3    Sasamoto, T.4
  • 31
    • 53649098294 scopus 로고    scopus 로고
    • Transitions between Airy1 and Airy2 processes and TASEP fluctuations
    • A. Borodin, P. L. Ferrari and T. Sasamoto, Transitions between Airy1 and Airy2 processes and TASEP fluctuations, Commun. Pure Appl. Math. 61 (2008) 1603-1629.
    • (2008) Commun. Pure Appl. Math. , vol.61 , pp. 1603-1629
    • Borodin, A.1    Ferrari, P.L.2    Sasamoto, T.3
  • 33
    • 46349095834 scopus 로고    scopus 로고
    • Airy kernel with two sets of parameters in directed percolation and random matrix theory
    • A. Borodin and S. Péché, Airy kernel with two sets of parameters in directed percolation and random matrix theory, J. Stat. Phys. 132 (2008) 275-290.
    • (2008) J. Stat. Phys. , vol.132 , pp. 275-290
    • Borodin, A.1    Péche, S.2
  • 34
    • 0000499144 scopus 로고
    • On the Bethe Ansatz for random directed polymers
    • J. P. Bouchaud and H. Orland, On the Bethe Ansatz for random directed polymers, J. Stat. Phys. 61 (1990) 877-888.
    • (1990) J. Stat. Phys. , vol.61 , pp. 877-888
    • Bouchaud, J.P.1    Orland, H.2
  • 35
    • 84980189802 scopus 로고
    • Maximal displacement of branching Brownian motion
    • M. Bramson, Maximal displacement of branching Brownian motion, Commun. Pure Appl. Math. 31 (1978) 531-581.
    • (1978) Commun. Pure Appl. Math. , vol.31 , pp. 531-581
    • Bramson, M.1
  • 36
    • 0036631309 scopus 로고    scopus 로고
    • Stationary blocking measures for one-dimensional nonzero mean exclusion processes
    • M. Bramson and T. Mountford, Stationary blocking measures for one-dimensional nonzero mean exclusion processes, Ann. Probab. 30 (2002) 1082-1130.
    • (2002) Ann. Probab. , vol.30 , pp. 1082-1130
    • Bramson, M.1    Mountford, T.2
  • 38
    • 47649097564 scopus 로고    scopus 로고
    • Dynamics of the attractive 1D Bose gas: Analytical treatment from integrability
    • P. Calabrese and J. S. Caux, Dynamics of the attractive 1D Bose gas: Analytical treatment from integrability, J. Stat. Mech. (2007) P08032.
    • (2007) J Stat. Mech. , pp. 08032
    • Calabrese, P.1    Caux, J.S.2
  • 39
    • 77953523639 scopus 로고    scopus 로고
    • Free-energy distribution of the directed polymer at high temperature
    • P. Calabrese, P. Le Doussal and A. Rosso, Free-energy distribution of the directed polymer at high temperature, Euro. Phys. Lett. 90 (2010) 20002.
    • (2010) Euro. Phys. Lett. , vol.90 , pp. 20002
    • Calabrese, P.1    Le Doussal, P.2    Rosso, A.3
  • 40
    • 79960631399 scopus 로고    scopus 로고
    • An exact solution for the KPZ equation with flat initial conditions
    • P. Calabrese and P. Le Doussal, An exact solution for the KPZ equation with flat initial conditions, Phys. Rev. Lett. 106 (2011) 250603.
    • (2011) Phys. Rev. Lett. , vol.106 , pp. 250603
    • Calabrese, P.1    Le Doussal, P.2
  • 41
    • 0034348846 scopus 로고    scopus 로고
    • Scaling limits of Wick ordered KPZ equation
    • T. Chan, Scaling limits of Wick ordered KPZ equation, Commun. Math. Phys. 209 (2000) 671-690.
    • (2000) Commun. Math. Phys. , vol.209 , pp. 671-690
    • Chan, T.1
  • 42
    • 21244503322 scopus 로고    scopus 로고
    • Probabilistic analysis of directed polymers in a random environment: A review
    • eds. T. Funaki and H. Osada (Math. Soc. Japan, Tokyo
    • F. Comets, T. Shiga and N. Yoshida, Probabilistic analysis of directed polymers in a random environment: A review, Stochastic Analysis on Large Scale Interacting Systems, eds. T. Funaki and H. Osada (Math. Soc. Japan, Tokyo, 2004), pp. 115-142.
    • (2004) Stochastic Analysis on Large Scale Interacting Systems , pp. 115-142
    • Comets, F.1    Shiga, T.2    Yoshida, N.3
  • 43
    • 33845476874 scopus 로고    scopus 로고
    • Directed polymers in random environment are diffusive at weak disorder
    • F. Comets and N. Yoshida, Directed polymers in random environment are diffusive at weak disorder, Ann. Probab. 34 (2006) 1746-1770.
    • (2006) Ann. Probab. , vol.34 , pp. 1746-1770
    • Comets, F.1    Yoshida, N.2
  • 44
    • 77954028711 scopus 로고    scopus 로고
    • Limit processes for TASEP with shocks and rarefaction fans
    • I. Corwin, P. L. Ferrari and S. Péché, Limit processes for TASEP with shocks and rarefaction fans, J. Stat. Phys. 140 (2010) 232-267.
    • (2010) J. Stat. Phys. , vol.140 , pp. 232-267
    • Corwin, P.L.1    Ferrari, S.2
  • 47
    • 85080859078 scopus 로고    scopus 로고
    • Corwin and J. Quastel, Universal distribution of fluctuations at the edge of the rarefaction fan, preprint, arXiv:
    • I. Corwin and J. Quastel, Universal distribution of fluctuations at the edge of the rarefaction fan, preprint, arXiv:1006.1338.
    • , vol.1 , pp. 1006-1338
  • 53
    • 34547667146 scopus 로고    scopus 로고
    • Non-equilibrium steady states: Fluctuations and large deviations of the density and of the current
    • B. Derrida, Non-equilibrium steady states: Fluctuations and large deviations of the density and of the current, J. Stat. Mech. (2007) P07023.
    • (2007) J. Stat. Mech. , pp. P07023
    • Derrida, B.1
  • 54
    • 11744342693 scopus 로고    scopus 로고
    • Exact large deviation function in the asymmetric exclusion process
    • B. Derrida and J. L. Lebowitz, Exact large deviation function in the asymmetric exclusion process, Phys. Rev. Lett. 80 (1998) 209-213.
    • (1998) Phys. Rev. Lett. , vol.80 , pp. 209-213
    • Derrida, B.1    Lebowitz, J.L.2
  • 55
    • 0001044333 scopus 로고
    • Polymers on disordered trees, spin glasses, and traveling waves
    • B. Derrida and H. Spohn, Polymers on disordered trees, spin glasses, and traveling waves, J. Stat. Phys. 51 (1988) 817-840.
    • (1988) J. Stat. Phys. , vol.51 , pp. 817-840
    • Derrida, B.1    Spohn, H.2
  • 56
    • 1542403830 scopus 로고    scopus 로고
    • On the Plancherel formula for the (discrete) Laplacian in a Weyl chamber with repulsive boundary conditions at the walls
    • J. F. van Diejen, On the Plancherel formula for the (discrete) Laplacian in a Weyl chamber with repulsive boundary conditions at the walls, Ann. H. Poincaré A 5 (2004) 135-168.
    • (2004) Ann. H. Poincaré A , vol.5 , pp. 135-168
    • Van Diejen, J.F.1
  • 57
    • 77954029182 scopus 로고    scopus 로고
    • On the largest-eigenvalue process for generalized wishart random matrices
    • A. B. Dieker and J.Warren, On the largest-eigenvalue process for generalized wishart random matrices, ALEA 6 (2009) 369-376.
    • (2009) ALEA , vol.6 , pp. 369-376
    • Dieker, A.B.1    Warren, J.2
  • 58
    • 84985316795 scopus 로고
    • A central limit theorem for the weakly asymmetric simple exclusion process
    • P. Dittrich and J. Gärtner, A central limit theorem for the weakly asymmetric simple exclusion process, Math. Nachr. 151 (1991) 79-93.
    • (1991) Math. Nachr. , vol.151 , pp. 79-93
    • Dittrich, P.1    Gärtner, J.2
  • 59
    • 21144479674 scopus 로고
    • Orthogonality and completeness of the Bethe Ansatz eigenstates of the nonlinear Schroedinger model
    • T. C. Dorlas, Orthogonality and completeness of the Bethe Ansatz eigenstates of the nonlinear Schroedinger model, Commun. Math. Phys. 154 (1993) 347-376.
    • (1993) Commun. Math. Phys. , vol.154 , pp. 347-376
    • Dorlas, T.C.1
  • 60
    • 77953500008 scopus 로고    scopus 로고
    • Bethe Ansatz derivation of the Tracy-Widom distribution for onedimensional directed polymers
    • V. Dotsenko, Bethe Ansatz derivation of the Tracy-Widom distribution for onedimensional directed polymers, Euro. Phys. Lett. 90 (2010) 20003.
    • (2010) Euro. Phys. Lett. , vol.90 , pp. 20003
    • Dotsenko, V.1
  • 61
    • 77950271971 scopus 로고    scopus 로고
    • Bethe Ansatz solution for one-dimensional directed polymers in random media
    • V. Dotsenko and B. Klumov, Bethe Ansatz solution for one-dimensional directed polymers in random media, J. Stat. Mech. (2010) P03022.
    • (2010) J. Stat. Mech. , pp. P03022
    • Dotsenko, V.1    Klumov, B.2
  • 62
    • 0041637573 scopus 로고
    • A Brownian-motion model for the eigenvalues of a random matrix
    • F. J. Dyson, A Brownian-motion model for the eigenvalues of a random matrix, J. Math. Phys. 3 (1962) 1191-1198.
    • (1962) J. Math. Phys. , vol.3 , pp. 1191-1198
    • Dyson, F.J.1
  • 63
    • 0001884774 scopus 로고
    • The surface statistics of a granular aggregate
    • S. Edwards and D. Wilkinson, The surface statistics of a granular aggregate, Proc. R. Soc. Lond. A 381 (1982) 17-31.
    • (1982) Proc. R. Soc. Lond. A , vol.381 , pp. 17-31
    • Edwards, S.1    Wilkinson, D.2
  • 65
  • 67
    • 33646754970 scopus 로고    scopus 로고
    • Scaling limit for the space-time covariance of the stationary totally asymmetric simple exclusion process
    • P. L. Ferrari and H. Spohn, Scaling limit for the space-time covariance of the stationary totally asymmetric simple exclusion process, Commun. Math. Phys. 65 (2006) 1-44.
    • (2006) Commun. Math. Phys. , vol.65 , pp. 1-44
    • Ferrari, P.L.1    Spohn, H.2
  • 68
    • 23744484022 scopus 로고    scopus 로고
    • A determinantal formula for the GOE Tracy-Widom distribution
    • P. L. Ferrari and H. Spohn, A determinantal formula for the GOE Tracy-Widom distribution, J. Phys. A 38 (2005) 557-561.
    • (2005) J. Phys. A , vol.38 , pp. 557-561
    • Ferrari, P.L.1    Spohn, H.2
  • 70
    • 0000768885 scopus 로고
    • Directed paths in random potential
    • D. S. Fisher and D. A. Huse, Directed paths in random potential, Phys. Rev. B. 43 (1991) 10728-10742.
    • (1991) Phys. Rev. B. , vol.43 , pp. 10728-10742
    • Fisher, D.S.1    Huse, D.A.2
  • 71
    • 4243603916 scopus 로고
    • Large-distance and long-time properties of a randomly stirred fluid
    • D. Forster, D. R. Nelson and M. J. Stephen, Large-distance and long-time properties of a randomly stirred fluid, Phys. Rev. A 16 (1977) 732-749.
    • (1977) Phys Rev. A , vol.16 , pp. 732-749
    • Forster, D.1    Nelson, D.R.2    Stephen, M.J.3
  • 72
    • 38249036614 scopus 로고
    • Convergence towards Burgers equation and propagation of chaos for weakly asymmetric exclusion process
    • J. Gärtner, Convergence towards Burgers equation and propagation of chaos for weakly asymmetric exclusion process, Stoch. Proc. Appl. 27 (1988) 233-260.
    • (1988) Stoch. Proc. Appl. , vol.27 , pp. 233-260
    • Gärtner, J.1
  • 73
    • 0003166713 scopus 로고
    • Symmetric functions and P-recursiveness
    • I. M. Gessel, Symmetric functions and P-recursiveness, J. Combin. Theory Ser. A 53 (1990) 257-285.
    • (1990) J. Combin. Theory Ser. A , vol.53 , pp. 257-285
    • Gessel, I.M.1
  • 76
    • 4243450938 scopus 로고
    • Bethe solution for the dynamical-scaling exponent of the noisy Burgers equation
    • L. H. Gwa and H. Spohn, Bethe solution for the dynamical-scaling exponent of the noisy Burgers equation, Phys. Rev. A 46 (1992) 844-854.
    • (1992) Phys. Rev. A , vol.46 , pp. 844-854
    • Gwa, L.H.1    Spohn, H.2
  • 77
    • 79952470930 scopus 로고    scopus 로고
    • Introduction to stochastic PDEs
    • available online at
    • M. Hairer, Introduction to stochastic PDEs, Lecture notes available online at www.hairer.org/Teaching.html
    • Lecture Notes
    • Hairer, M.1
  • 79
    • 0009207670 scopus 로고
    • Directed polymers in random media: Probability distributions
    • T. Halpin Healy, Directed polymers in random media: Probability distributions, Phys. Rev. A 44 (1991) 3415-3418.
    • (1991) Phys. Rev. A , vol.44 , pp. 3415-3418
    • Halpin Healy, T.1
  • 80
    • 0012575045 scopus 로고
    • Kinetic roughening, stochastic growth, directed polymers and all that
    • T. Halpin Healy and Y. Z. Zhang, Kinetic roughening, stochastic growth, directed polymers and all that, Phys. Rep. 254 (1995) 215-415.
    • (1995) Phys Rep. , vol.254 , pp. 215-415
    • Halpin Healy, T.1    Zhang, Y.Z.2
  • 84
    • 85080904125 scopus 로고    scopus 로고
    • Random Polymers ecole d'Eté de Probabilités de Saint-Flour
    • Springer, Berlin
    • F. den Hollander, Random Polymers, Ecole d'Eté de Probabilités de Saint-Flour, Lecture Notes in Mathematics, Vol. XXXVII (Springer, Berlin, 2007).
    • (2007) Lecture Notes in Mathematics , vol.37
    • Den Hollander, F.1
  • 85
    • 0000878714 scopus 로고
    • Pinning and roughening of domain walls in Ising systems due to random impurities
    • D. A. Huse and C. L. Henley, Pinning and roughening of domain walls in Ising systems due to random impurities, Phys. Rev. Lett. 54 (1985) 2708-2711.
    • (1985) Phys. Rev. Lett. , vol.54 , pp. 2708-2711
    • Huse, D.A.1    Henley, C.L.2
  • 87
    • 0001359551 scopus 로고    scopus 로고
    • Similarity-detection and localization
    • T. Hwa and M. Lassig, Similarity-detection and localization, Phys. Rev. Lett. 76 (1996) 2591-2594.
    • (1996) Phys. Rev. Lett. , vol.76 , pp. 2591-2594
    • Hwa, T.1    Lassig, M.2
  • 88
    • 4844224385 scopus 로고    scopus 로고
    • Fluctuations of the one-dimensional polynuclear growth model with external sources
    • T. Imamura and T. Sasamoto, Fluctuations of the one-dimensional polynuclear growth model with external sources, Nucl. Phys. B 699 (2004) 503-544.
    • (2004) Nucl. Phys. B , vol.699 , pp. 503-544
    • Imamura, T.1    Sasamoto, T.2
  • 90
    • 0001100265 scopus 로고
    • Diffusion of directed polymers in a random environment
    • J. Z. Imbrie and T. Spencer, Diffusion of directed polymers in a random environment, J. Stat. Phys. 52 (1988) 609-626.
    • (1988) J. Stat. Phys. , vol.52 , pp. 609-626
    • Imbrie, J.Z.1    Spencer, T.2
  • 91
    • 0034340689 scopus 로고    scopus 로고
    • Shape fluctuations and random matrices
    • K. Johansson, Shape fluctuations and random matrices, Commun. Math. Phys. 209 (2000) 437-476.
    • (2000) Commun. Math. Phys. , vol.209 , pp. 437-476
    • Johansson, K.1
  • 92
    • 0242592942 scopus 로고    scopus 로고
    • Discrete polynuclear growth and determinantal processes
    • K. Johansson, Discrete polynuclear growth and determinantal processes, Commun. Math. Phys. 242 (2003) 277-329.
    • (2003) Commun. Math. Phys. , vol.242 , pp. 277-329
    • Johansson, K.1
  • 94
    • 5544248074 scopus 로고
    • Replica-Bethe Ansatz studies of two-dimensional interfaces with quenched random impurities
    • M. Kardar, Replica-Bethe Ansatz studies of two-dimensional interfaces with quenched random impurities, Nucl. Phys. B 290 (1987) 582-602.
    • (1987) Nucl. Phys. B , vol.290 , pp. 582-602
    • Kardar, M.1
  • 95
    • 0001257558 scopus 로고
    • Roughening by impurities at finite temperatures
    • M. Kardar, Roughening by impurities at finite temperatures, Phys. Rev. Lett. 55 (1985) 2923.
    • (1985) Phys. Rev. Lett. , vol.55 , pp. 2923
    • Kardar, M.1
  • 96
    • 4243979739 scopus 로고
    • Dynamic scaling of growing interfaces
    • M. Kardar, G. Parisi and Y. Z. Zhang, Dynamic scaling of growing interfaces, Phys. Rev. Lett. 56 (1986) 889-892.
    • (1986) Phys. Rev. Lett. , vol.56 , pp. 889-892
    • Kardar, M.1    Parisi, G.2    Zhang, Y.Z.3
  • 97
    • 0003355892 scopus 로고
    • Kinetics of Ising models
    • eds. C. Domb and M. S. Green (Academic Press
    • K. Kawasaki, Kinetics of Ising models, Phase Transitions and Critical Phenomena, eds. C. Domb and M. S. Green (Academic Press, 1972).
    • (1972) Phase Transitions and Critical Phenomena
    • Kawasaki, K.1
  • 98
    • 0000264803 scopus 로고
    • Aspects of first-passage percolation
    • H. Kesten, Aspects of first-passage percolation, Lecture Notes in Mathematics, Vol. 1180 (1986), pp. 125-264.
    • (1986) Lecture Notes in Mathematics , vol.1180 , pp. 125-264
    • Kesten, H.1
  • 99
    • 0001385836 scopus 로고
    • Zero-temperature directed polymers in a random potential
    • J. M. Kim, M. A. Moore and A. J. Bray, Zero-temperature directed polymers in a random potential, Phys. Rev. A 44 (1991) 2345-2351.
    • (1991) Phys Rev. A , vol.44 , pp. 2345-2351
    • Kim, J.M.1    Moore, M.A.2    Bray, A.J.3
  • 103
    • 0000535030 scopus 로고
    • Stochastic partial differential equations for some measurevalued diffusions
    • N. Konno and T. Shiga, Stochastic partial differential equations for some measurevalued diffusions, Probab. Theory Relat. Fields 79 (1988) 201-225.
    • (1988) Probab. Theory Relat. Fields , vol.79 , pp. 201-225
    • Konno, N.1    Shiga, T.2
  • 104
    • 78649644408 scopus 로고    scopus 로고
    • A pedestrian's view on interacting particle systems, KPZ universality, and random matrices
    • T. Kriecherbauer and J. Krug, A pedestrian's view on interacting particle systems, KPZ universality, and random matrices, J. Phys. A: Math. Theor. 43 (2010) 403001.
    • (2010) J. Phys. A: Math. Theor. , vol.43 , pp. 403001
    • Kriecherbauer, T.1    Krug, J.2
  • 105
    • 0003067639 scopus 로고
    • Healy Amplitude universality for driven interfaces and directed polymers in random media
    • J. Krug, P. Meakin and T. Halpin Healy, Amplitude universality for driven interfaces and directed polymers in random media, Phys. Rev. A 45 (1992) 638-653.
    • (1992) Phys. Rev. A , vol.45 , pp. 638-653
    • Krug, J.1    Meakin, P.2    Halpin, T.3
  • 106
    • 0003067890 scopus 로고
    • Kinetic roughening of growing surfaces
    • ed. C. Godréche (Cambridge University Press
    • H. Krug and H. Spohn, Kinetic roughening of growing surfaces, Solids Far from Equilibrium, ed. C. Godréche (Cambridge University Press, 1991), pp. 412-525.
    • (1991) Solids Far from Equilibrium , pp. 412-525
    • Krug, H.1    Spohn, H.2
  • 107
    • 0041383633 scopus 로고    scopus 로고
    • Dynamic scaling behavior of a growing self-affine fractal interface in a paper-towel-wetting experiment
    • T. H. Kwon, A. E. Hopkins and S. E. O'Donnell, Dynamic scaling behavior of a growing self-affine fractal interface in a paper-towel-wetting experiment, Phys. Rev. E 54 (1996) 685-690.
    • (1996) Phys Rev. E , vol.54 , pp. 685-690
    • Kwon, T.H.1    Hopkins, A.E.2    O'Donnell, S.E.3
  • 108
    • 76349109024 scopus 로고    scopus 로고
    • New bounds for the free energy of directed polymer in dimension 1 + 1 and 1 + 2
    • H. Lacoin, New bounds for the free energy of directed polymer in dimension 1 + 1 and 1 + 2, Commun. Math. Phys. 294 (2010) 471-503.
    • (2010) Commun. Math. Phys. , vol.294 , pp. 471-503
    • Lacoin, H.1
  • 109
    • 0343130876 scopus 로고    scopus 로고
    • On growth, disorder, and field theory
    • M. Lässig, On growth, disorder, and field theory, J. Phys. C 10 (1998) 9905-9950.
    • (1998) J Phys. C , vol.10 , pp. 9905-9950
    • Lässig, M.1
  • 111
    • 21444460424 scopus 로고    scopus 로고
    • Superdiffusivity in first-passage percolation Probab
    • C. Licea, C. Newman and M. Piza, Superdiffusivity in first-passage percolation, Probab. Theory Relat. Fields 106 (1996) 559-591.
    • (1996) Theory Relat. Fields , vol.106 , pp. 559-591
    • Licea, C.1    Newman, C.2    Piza, M.3
  • 112
    • 26344439240 scopus 로고
    • Exact analysis of an interacting Bose gas. I. the general solution and the ground state
    • E. H. Lieb and W. Liniger, Exact analysis of an interacting Bose gas. I. The general solution and the ground state, Phys. Rev. Lett. 130 (1963) 1605-1616.
    • (1963) Phys. Rev. Lett. , vol.130 , pp. 1605-1616
    • Lieb, E.H.1    Liniger, W.2
  • 113
    • 0004139016 scopus 로고    scopus 로고
    • Springer, Berlin, reprint of, original edition
    • T. M. Liggett, Interacting Particle Systems (Springer, Berlin, reprint of 1985 original edition, 2005).
    • (2005) Interacting Particle Systems , vol.1985
    • Liggett, T.M.1
  • 117
    • 23844443186 scopus 로고    scopus 로고
    • Experimental determination of KPZ height-fluctuation distributions
    • L. Miettinen, M. Myllys, J. Merikoski and J. Timonen, Experimental determination of KPZ height-fluctuation distributions, Eur. Phys. J. B 46 (2005) 55-60.
    • (2005) Eur. Phys. J. B , vol.46 , pp. 55-60
    • Miettinen, L.1    Myllys, M.2    Merikoski, J.3    Timonen, J.4
  • 118
    • 40849100508 scopus 로고    scopus 로고
    • Random matrices, the Ulam problem, directed polymers and growth models, and sequence matching
    • S. N. Majumdar, Random matrices, the Ulam problem, directed polymers and growth models, and sequence matching, in Les Houches Summer School Proceeding 85 (2007) 179-216.
    • (2007) Les Houches Summer School Proceeding , vol.85 , pp. 179-216
    • Majumdar, S.N.1
  • 119
    • 40749111078 scopus 로고    scopus 로고
    • Bethe Ansatz in the Bernoulli matching model of random sequence alignment
    • S. N. Majumdar, K. Mallick and S. Nechaev, Bethe Ansatz in the Bernoulli matching model of random sequence alignment, Phys. Rev. E 77 (2008) 011110.
    • (2008) Phys. Rev. E , vol.77 , pp. 011110
    • Majumdar, S.N.1    Mallick, K.2    Nechaev, S.3
  • 121
    • 1442298890 scopus 로고
    • Study of exactly soluble one-dimensional N-body problems
    • J. B. McGuire, Study of exactly soluble one-dimensional N-body problems, J. Math. Phys. 5 (1964) 622.
    • (1964) J. Math. Phys. , vol.5 , pp. 622
    • McGuire, J.B.1
  • 122
    • 0009319932 scopus 로고
    • On the support of solutions to the heat equation with noise
    • C. Mueller, On the support of solutions to the heat equation with noise, Stochastics 37 (1991) 225-246.
    • (1991) Stochastics , vol.37 , pp. 225-246
    • Mueller, C.1
  • 123
    • 4844231719 scopus 로고    scopus 로고
    • Asymmetric simple exclusion process and modified random matrix ensembles
    • T. Nagao and T. Sasamoto, Asymmetric simple exclusion process and modified random matrix ensembles, Nuclear Phys. B 699 (2004) 487-502.
    • (2004) Nuclear Phys. B , vol.699 , pp. 487-502
    • Nagao, T.1    Sasamoto, T.2
  • 124
    • 0001113761 scopus 로고    scopus 로고
    • From ballistic deposition to the Kardar-Parisi-Zhang equation through a limiting procedure
    • T. Nagatani, From ballistic deposition to the Kardar-Parisi-Zhang equation through a limiting procedure, Phys. Rev. E 58 (1998) 700-703.
    • (1998) Phys. Rev. E , vol.58 , pp. 700-703
    • Nagatani, T.1
  • 125
    • 0001754757 scopus 로고
    • Divergence of shape fluctuations in two dimensions
    • C. Newman and M. Piza, Divergence of shape fluctuations in two dimensions, Ann. Probab. 23 (1995) 977-1005.
    • (1995) Ann. Probab. , vol.23 , pp. 977-1005
    • Newman, C.1    Piza, M.2
  • 129
    • 0039864907 scopus 로고    scopus 로고
    • On longest increasing subsequences in random permutations
    • eds E. L. Grinberg, S. Berhanu, M. Knopp, G. Mendoza and E. T. Quinto (American Mathematical Society
    • A. M. Odlyzko and E. M. Rains, On longest increasing subsequences in random permutations, in Analysis, Geometry, Number Theory: The Mathematics of Leon Ehrenpreis, eds. E. L. Grinberg, S. Berhanu, M. Knopp, G. Mendoza and E. T. Quinto (American Mathematical Society, 2000), pp. 439-451.
    • (2000) Analysis, Geometry, Number Theory: The Mathematics of Leon Ehrenpreis , pp. 439-451
    • Odlyzko, A.M.1    Rains, E.M.2
  • 131
    • 0000312963 scopus 로고
    • Exact derivation of the Kardar-Parisi-Zhang equation from the restricted solid-on-solid model
    • K. Park and B. Kahng, Exact derivation of the Kardar-Parisi-Zhang equation from the restricted solid-on-solid model, Phys. Rev. E 51 (1995) 796-798.
    • (1995) Phys. Rev. E , vol.51 , pp. 796-798
    • Park, K.1    Kahng, B.2
  • 133
    • 0000439075 scopus 로고    scopus 로고
    • Universal distributions for growth processes in 1 + 1 dimensions and random matrices
    • M. Prähofer and H. Spohn, Universal distributions for growth processes in 1 + 1 dimensions and random matrices, Phys. Rev. Lett. 84 (2000) 4882-4885.
    • (2000) Phys. Rev. Lett. , vol.84 , pp. 4882-4885
    • Prähofer, M.1    Spohn, H.2
  • 134
    • 0012620162 scopus 로고    scopus 로고
    • Current fluctuations for the totally asymmetric simple exclusion process, in and out of equilibrium
    • ed. V. Sidoravicius
    • M. Prähofer and H. Spohn, Current fluctuations for the totally asymmetric simple exclusion process, in and out of equilibrium, ed. V. Sidoravicius, Progress Probab. 51 (2002) 185-204.
    • (2002) Progress Probab. , vol.51 , pp. 185-204
    • Prähofer, M.1    Spohn, H.2
  • 135
    • 0141450340 scopus 로고    scopus 로고
    • Scale invariance of the PNG droplet and the Airy process
    • M. Prähofer and H. Spohn, Scale invariance of the PNG droplet and the Airy process, J. Stat. Phys. 108 (2002) 1071-1106.
    • (2002) J. Stat. Phys. , vol.108 , pp. 1071-1106
    • Prähofer, M.1    Spohn, H.2
  • 136
    • 79751501755 scopus 로고    scopus 로고
    • Two-point generating function of the free energy for a directed polymer in a random medium
    • S. Prolhac and H. Spohn, Two-point generating function of the free energy for a directed polymer in a random medium, J. Stat. Mech. (2011) P01031.
    • (2011) J. Stat. Mech. , pp. 1031
    • Prolhac, S.1    Spohn, H.2
  • 137
    • 79953704244 scopus 로고    scopus 로고
    • The one-dimensional KPZ equation and the Airy process
    • S. Prolhac and H. Spohn, The one-dimensional KPZ equation and the Airy process, J. Stat. Mech. (2011) P03020.
    • (2011) J. Stat. Mech. , pp. 03020
    • Prolhac, S.1    Spohn, H.2
  • 138
    • 79961113465 scopus 로고    scopus 로고
    • The height distribution of the KPZ equation with sharp wedge initial condition: Numerical evaluations
    • S. Prolhac and H. Spohn, The height distribution of the KPZ equation with sharp wedge initial condition: Numerical evaluations, Phys. Rev. E 84 (2011) 011119.
    • (2011) Phys. Rev. E , vol.84 , pp. 011119
    • Prolhac, S.1    Spohn, H.2
  • 139
    • 84856275576 scopus 로고    scopus 로고
    • A note on the diffusivity of finite-range asymmetric exclusion processes on Z, in and out of equilibrium
    • ed. V. Sidoravicius
    • J. Quastel and B. Valko, A note on the diffusivity of finite-range asymmetric exclusion processes on Z, in and out of equilibrium, ed. V. Sidoravicius, Progress Probab. 60 (2008) 543-549.
    • (2008) Progress Probab. , vol.60 , pp. 543-549
    • Quastel, J.1    Valko, B.2
  • 140
    • 33646944980 scopus 로고
    • Hydrodynamic limits for attractive particle systems on Zd
    • F. Rezakhanlou, Hydrodynamic limits for attractive particle systems on Zd, Commun. Math. Phys. 140 (1991) 417-448.
    • (1991) Commun. Math. Phys. , vol.140 , pp. 417-448
    • Rezakhanlou, F.1
  • 141
    • 33645840905 scopus 로고
    • Non-equilibrium behavior of a many particle process: Density profile and the local equilibrium
    • H. Rost, Non-equilibrium behavior of a many particle process: Density profile and the local equilibrium, Z. Wahrsch. Verw. Gebiete 58 (1981) 41-53.
    • (1981) Z. Wahrsch. Verw. Gebiete , vol.58 , pp. 41-53
    • Rost, H.1
  • 142
    • 33244475773 scopus 로고    scopus 로고
    • Score statistics of global sequence alignment from the energy distribution of a modified directed polymer and directed percolation problem
    • M. E. Sardiu, G. Alves and Y. K. Yu, Score statistics of global sequence alignment from the energy distribution of a modified directed polymer and directed percolation problem, Phys. Rev. E 72 (2005) 061917.
    • (2005) Phys Rev. E , vol.72 , pp. 061917
    • Sardiu, M.E.1    Alves, G.2    Yu, Y.K.3
  • 143
    • 23744500397 scopus 로고    scopus 로고
    • Spatial correlations of the 1D KPZ surface on a flat substrate
    • T. Sasamoto, Spatial correlations of the 1D KPZ surface on a flat substrate, J. Phys. A 38 549-556.
    • J. Phys. A , vol.38 , pp. 549-556
    • Sasamoto, T.1
  • 144
    • 77952885302 scopus 로고    scopus 로고
    • Exact height distributions for the KPZ equation with narrow wedge initial condition
    • T. Sasamoto and H. Spohn, Exact height distributions for the KPZ equation with narrow wedge initial condition, Nucl. Phys. B 834 (2010) 523-542.
    • (2010) Nucl. Phys. B , vol.834 , pp. 523-542
    • Sasamoto, T.1    Spohn, H.2
  • 145
    • 77953526534 scopus 로고    scopus 로고
    • One-dimensional KPZ equation: An exact solution and its universality
    • T. Sasamoto and H. Spohn, One-dimensional KPZ equation: An exact solution and its universality, Phys. Rev. Lett. 104 (2010) 23.
    • (2010) Phys. Rev. Lett. , vol.104 , pp. 23
    • Sasamoto, T.1    Spohn, H.2
  • 146
    • 77954032129 scopus 로고    scopus 로고
    • The crossover regime for the weakly asymmetric simple exclusion process
    • T. Sasamoto and H. Spohn, The crossover regime for the weakly asymmetric simple exclusion process, J. Stat. Phys. 140 (2010) 209-231.
    • (2010) J. Stat. Phys. , vol.140 , pp. 209-231
    • Sasamoto, T.1    Spohn, H.2
  • 147
    • 78650408621 scopus 로고    scopus 로고
    • The 1 + 1-dimensional Kardar-Parisi-Zhang equation and its universality class
    • T. Sasamoto and H. Spohn, The 1 + 1-dimensional Kardar-Parisi-Zhang equation and its universality class, J. Stat. Mech. (2010) P11013.
    • (2010) J. Stat. Mech. , pp. 11013
    • Sasamoto, T.1    Spohn, H.2
  • 148
    • 0040238394 scopus 로고    scopus 로고
    • Exact solution of the master equation for the asymmetric exclusion process
    • G. M. Schütz, Exact solution of the master equation for the asymmetric exclusion process, J. Stat. Phys. 88 (1997) 427-445.
    • (1997) J. Stat. Phys. , vol.88 , pp. 427-445
    • Schütz, G.M.1
  • 151
    • 0000313893 scopus 로고
    • A remark concerning random walks with random potentials
    • Y. Sinai, A remark concerning random walks with random potentials, Fund. Math. 147 (1995) 173-180.
    • (1995) Fund. Math. , vol.147 , pp. 173-180
    • Sinai, Y.1
  • 152
    • 38149032783 scopus 로고    scopus 로고
    • The algebraic Bethe Ansatz and quantum integrable systems
    • N. Slavnov, The algebraic Bethe Ansatz and quantum integrable systems, Russ. Math. Surv. 62 (2007) 727.
    • (2007) Russ. Math. Surv. , vol.62 , pp. 727
    • Slavnov, N.1
  • 153
    • 0040261379 scopus 로고
    • Interaction of Markov processes
    • F. Spitzer, Interaction of Markov processes, Adv. Math. 5 (1970) 246-290.
    • (1970) Adv. Math. , vol.5 , pp. 246-290
    • Spitzer, F.1
  • 155
    • 33745660065 scopus 로고    scopus 로고
    • Exact solutions for KPZ-type growth processes random matrices, and equilibrium shapes of crystals
    • H. Spohn, Exact solutions for KPZ-type growth processes, random matrices, and equilibrium shapes of crystals, Phys. A 369 (2006) 71-99.
    • (2006) Phys. A , vol.369 , pp. 71-99
    • Spohn, H.1
  • 156
    • 77953517950 scopus 로고    scopus 로고
    • Universal fluctuations of growing interfaces: Evidence in turbulent liquid crystals
    • K. Takeuchi and M. Sano, Universal fluctuations of growing interfaces: Evidence in turbulent liquid crystals, Phys. Rev. Lett. 104 (2010) 230601.
    • (2010) Phys. Rev. Lett. , vol.104 , pp. 230601
    • Takeuchi, K.1    Sano, M.2
  • 157
    • 81155130410 scopus 로고    scopus 로고
    • Growing interfaces uncover universal fluctuations behind scale invariance
    • K. Takeuchi, M. Sano, T. Sasamoto and H. Spohn, Growing interfaces uncover universal fluctuations behind scale invariance, Sci. Rep. 34 (2011).
    • (2011) Sci. Rep. , vol.34
    • Takeuchi, K.1    Sano, M.2    Sasamoto, T.3    Spohn, H.4
  • 158
    • 33645683399 scopus 로고    scopus 로고
    • The Parisi formula
    • M. Talagrand, The Parisi formula, Ann. Math. 163 (2005) 221-263.
    • (2005) Ann. Math. , vol.163 , pp. 221-263
    • Talagrand, M.1
  • 159
    • 27644532196 scopus 로고
    • Level-spacing distributions and the Airy kernel
    • C. Tracy and H. Widom, Level-spacing distributions and the Airy kernel, Commun. Math. Phys. 159 (1994) 151-174.
    • (1994) Commun. Math. Phys. , vol.159 , pp. 151-174
    • Tracy, C.1    Widom, H.2
  • 160
    • 41149087607 scopus 로고    scopus 로고
    • Integral formulas for the asymmetric simple exclusion process
    • C. Tracy and H. Widom, Integral formulas for the asymmetric simple exclusion process, Commun. Math. Phys. 279 (2008) 815-844.
    • (2008) Commun. Math. Phys. , vol.279 , pp. 815-844
    • Tracy, C.1    Widom, H.2
  • 161
    • 46349105749 scopus 로고    scopus 로고
    • A Fredholm determinant representation in ASEP
    • C. Tracy and H. Widom, A Fredholm determinant representation in ASEP, J. Stat. Phys. 132 (2008) 291-300.
    • (2008) J. Stat. Phys. , vol.132 , pp. 291-300
    • Tracy, C.1    Widom, H.2
  • 162
    • 70349658863 scopus 로고    scopus 로고
    • Asymptotics in ASEP with step initial condition
    • C. Tracy and H.Widom, Asymptotics in ASEP with step initial condition, Commun. Math. Phys. 290 (2009) 129-154.
    • (2009) Commun. Math. Phys. , vol.290 , pp. 129-154
    • Tracy, C.1    Widom, H.2
  • 163
    • 77954865787 scopus 로고    scopus 로고
    • Formulas for ASEP with two-sided Bernoulli initial condition
    • C. Tracy and H. Widom, Formulas for ASEP with two-sided Bernoulli initial condition, J. Stat. Phys. 140 (2010) 619-634.
    • (2010) J. Stat. Phys. , vol.140 , pp. 619-634
    • Tracy, C.1    Widom, H.2
  • 164
    • 3042655531 scopus 로고    scopus 로고
    • A system of differential equations for the Airy process
    • C. Tracy and H. Widom, A system of differential equations for the Airy process, Electron. Commun. Probab. 8 (2003) 93-98.
    • (2003) Electron. Commun. Probab. , vol.8 , pp. 93-98
    • Tracy, C.1    Widom, H.2
  • 165
    • 79952078384 scopus 로고    scopus 로고
    • On ASEP with periodic step Bernoulli initial condition
    • C. Tracy and H. Widom, On ASEP with periodic step Bernoulli initial condition, J. Math. Phys. 52 (2011) 023303.
    • (2011) J. Math. Phys. , vol.52 , pp. 023303
    • Tracy, C.1    Widom, H.2
  • 166
    • 64549148340 scopus 로고    scopus 로고
    • The dynamics of the one-dimensional delta-function Bose gas
    • C. Tracy and H. Widom, The dynamics of the one-dimensional delta-function Bose gas, J. Phys. A 41 (2008) 485204.
    • (2008) J. Phys. A , vol.41 , pp. 485204
    • Tracy, C.1    Widom, H.2
  • 168
    • 0041509046 scopus 로고    scopus 로고
    • The universality classes in growth of iron nitride thin films deposited by magnetron sputtering
    • X. Wang, W. Zheng and L. Gao, The universality classes in growth of iron nitride thin films deposited by magnetron sputtering, Mater. Chem. Phys. 82 (2003) 254-257.
    • (2003) Mater. Chem. Phys. , vol.82 , pp. 254-257
    • Wang, X.1    Zheng, W.2    Gao, L.3
  • 169
    • 0031532442 scopus 로고    scopus 로고
    • Self-affinity for the growing interface of bacterial colonies
    • J. Wakita, H. Itoh, T. Matsuyama and M. Matsushita, Self-affinity for the growing interface of bacterial colonies, J. Phys. Soc. Jpn. 66 (1997) 67-72.
    • (1997) J. Phys. Soc. Jpn. , vol.66 , pp. 67-72
    • Wakita, J.1    Itoh, H.2    Matsuyama, T.3    Matsushita, M.4
  • 170
    • 33244465143 scopus 로고    scopus 로고
    • Large deviations for the asymmetric simple exclusion process
    • S. R. S. Varadhan, Large deviations for the asymmetric simple exclusion process, Adv. Stud. Pure Math. 39 (2004) 1-27.
    • (2004) Adv. Stud. Pure Math. , vol.39 , pp. 1-27
    • Varadhan, S.R.S.1


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