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Volumn 235, Issue 1-2 SPEC. ISS., 2007, Pages 168-206

Fermionic construction of tau functions and random processes

Author keywords

Driven diffusive motion; Free fermions; Integrable systems; Random processes; Stochastic dynamics; Tau function

Indexed keywords

FERMIONS; FUNCTION EVALUATION; MATHEMATICAL MODELS; SOLITONS;

EID: 35048834693     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physd.2007.05.011     Document Type: Article
Times cited : (10)

References (66)
  • 6
    • 0034377725 scopus 로고    scopus 로고
    • Random vicious walk and random matrices
    • Baik J. Random vicious walk and random matrices. Comm. Pure Appl. Math. 53 11 (2000) 1185-1410
    • (2000) Comm. Pure Appl. Math. , vol.53 , Issue.11 , pp. 1185-1410
    • Baik, J.1
  • 7
    • 0346995411 scopus 로고    scopus 로고
    • Differential systems for biorthogonal polynomials appearing in 2-matrix models, and the associated Riemann-Hilbert problem
    • Bertola M., Eynard B., and Harnad J. Differential systems for biorthogonal polynomials appearing in 2-matrix models, and the associated Riemann-Hilbert problem. Comm. Math. Phys. 243 (2003) 193-240
    • (2003) Comm. Math. Phys. , vol.243 , pp. 193-240
    • Bertola, M.1    Eynard, B.2    Harnad, J.3
  • 15
    • 34250142002 scopus 로고
    • Walks, walls, wetting and melting
    • Fisher M. Walks, walls, wetting and melting. J. Stat. Phys. 34 (1984) 667-729
    • (1984) J. Stat. Phys. , vol.34 , pp. 667-729
    • Fisher, M.1
  • 16
    • 0001283085 scopus 로고
    • The isomonodromy approach to matrix models in 2D quantum gravity
    • Fokas A.S., Its A.R., and Kitaev A.V. The isomonodromy approach to matrix models in 2D quantum gravity. Comm. Math. Phys. 147 (1992) 395-430
    • (1992) Comm. Math. Phys. , vol.147 , pp. 395-430
    • Fokas, A.S.1    Its, A.R.2    Kitaev, A.V.3
  • 17
    • 35048854846 scopus 로고    scopus 로고
    • P.J. Forrester, Log Gases and Random Matrices. http://www.ms.unimelb.edu.au/ matpjf.matpjf.html (in preparation)
  • 21
    • 11944258149 scopus 로고
    • Six-vertex model, roughened surfaces and an asymmetric spin hamiltonian?
    • Gwa K.-H., and Spohn H. Six-vertex model, roughened surfaces and an asymmetric spin hamiltonian?. Phys. Rev. Lett. 68 (1992) 725-728
    • (1992) Phys. Rev. Lett. , vol.68 , pp. 725-728
    • Gwa, K.-H.1    Spohn, H.2
  • 22
    • 4243450938 scopus 로고
    • Bethe solution for the dynamical-scaling exponent of the noisy Burgers equation
    • Gwa K.-H., and Spohn H. Bethe solution for the dynamical-scaling exponent of the noisy Burgers equation. Phys. Rev. A 46 (1992) 844-854
    • (1992) Phys. Rev. , vol.A 46 , pp. 844-854
    • Gwa, K.-H.1    Spohn, H.2
  • 23
    • 10144233299 scopus 로고    scopus 로고
    • Janossy densities, multimatrix spacing distributions and Fredholm resolvents
    • Harnad J. Janossy densities, multimatrix spacing distributions and Fredholm resolvents. Int. Math. Res. Not. 48 (2004) 2599-2609
    • (2004) Int. Math. Res. Not. , vol.48 , pp. 2599-2609
    • Harnad, J.1
  • 24
    • 21844488807 scopus 로고
    • Dual isomonodromic deformations and moment maps into loop algebras
    • Harnad J. Dual isomonodromic deformations and moment maps into loop algebras. Comm. Math. Phys. 166 (1994) 337-365
    • (1994) Comm. Math. Phys. , vol.166 , pp. 337-365
    • Harnad, J.1
  • 25
    • 0036011686 scopus 로고    scopus 로고
    • Integrable Fredholm operators and dual isomonodromic deformations
    • Harnad J., and Its A.R. Integrable Fredholm operators and dual isomonodromic deformations. Comm. Math. Phys. 226 (2002) 497-530
    • (2002) Comm. Math. Phys. , vol.226 , pp. 497-530
    • Harnad, J.1    Its, A.R.2
  • 26
    • 3943071072 scopus 로고    scopus 로고
    • Scalar products of symmetric functions and matrix integrals
    • Harnad J., and Orlov A.Yu. Scalar products of symmetric functions and matrix integrals. Theoret. and Math. Phys. 137 (2003) 1676-1690
    • (2003) Theoret. and Math. Phys. , vol.137 , pp. 1676-1690
    • Harnad, J.1    Orlov, A.Yu.2
  • 27
    • 3943071072 scopus 로고    scopus 로고
    • Scalar products of symmetric functions and matrix integrals
    • nlin.SI/0211051
    • Harnad J.P., and Orlov A.Yu. Scalar products of symmetric functions and matrix integrals. Theoret. and Math. Phys. 137 (2003) 1676-1690. nlin.SI/0211051
    • (2003) Theoret. and Math. Phys. , vol.137 , pp. 1676-1690
    • Harnad, J.P.1    Orlov, A.Yu.2
  • 28
    • 33745557829 scopus 로고    scopus 로고
    • Fermionic construction of partition functions for two-matrix models and perturbative Schur function expansions
    • Harnad J., and Orlov A.Yu. Fermionic construction of partition functions for two-matrix models and perturbative Schur function expansions. J. Phys. A (2006) 8783-8810
    • (2006) J. Phys. , vol.A , pp. 8783-8810
    • Harnad, J.1    Orlov, A.Yu.2
  • 29
    • 35048864135 scopus 로고    scopus 로고
    • J.P. Harnad, A.Yu. Orlov, Evaluation of asymptotics of correlation functions for random turn Brownian motion (in preparation)
  • 30
    • 35048880389 scopus 로고    scopus 로고
    • J.P. Harnad, J.W. van de Leur, A.Yu. Orlov, Fermionic construction of BKP tau functions for random processes (in preparation)
  • 31
    • 35048853342 scopus 로고    scopus 로고
    • J.P. Harnad, A.Yu. Orlov, Fermionic construction of partition function for multi-matrix models and multi-component TL hierarchy, 2005. Preprint
  • 33
    • 0034340689 scopus 로고    scopus 로고
    • Shape fluctuations and random matrices
    • Johansson K. Shape fluctuations and random matrices. Comm. Math. Phys. 209 (2000) 437-476
    • (2000) Comm. Math. Phys. , vol.209 , pp. 437-476
    • Johansson, K.1
  • 34
    • 0003137426 scopus 로고
    • The n-component K P hierarchy and representation theory
    • Important Developments in Soliton Theory. Fokas A.S., and Zakharov V.E. (Eds)
    • Kac V.G., and van de Leur J.W. The n-component K P hierarchy and representation theory. In: Fokas A.S., and Zakharov V.E. (Eds). Important Developments in Soliton Theory. Springer Series in Nonlinear Dynamics (1993) 302-343
    • (1993) Springer Series in Nonlinear Dynamics , pp. 302-343
    • Kac, V.G.1    van de Leur, J.W.2
  • 35
    • 0003193362 scopus 로고    scopus 로고
    • The geometry of spinors and multicomponent BKP and DKP hierarchies
    • Kac V.G., and van de Leur J.W. The geometry of spinors and multicomponent BKP and DKP hierarchies. CRM Proceedings and Lecture Notes vol. 14 (1998) 159-202
    • (1998) CRM Proceedings and Lecture Notes , vol.14 , pp. 159-202
    • Kac, V.G.1    van de Leur, J.W.2
  • 38
    • 0000057952 scopus 로고
    • Asymptotics of the Plancherel measure of the symmetric group and the limitinf form of Young tableaux
    • Vershik A.M., and Kerov S.V. Asymptotics of the Plancherel measure of the symmetric group and the limitinf form of Young tableaux. Soviet Math. Dokl. 18 (1977) 527-531
    • (1977) Soviet Math. Dokl. , vol.18 , pp. 527-531
    • Vershik, A.M.1    Kerov, S.V.2
  • 39
    • 34250123019 scopus 로고
    • Asymptotics of the largest and the typical dimensions of the irreducible representations of a symmetric group
    • Vershik A.M., and Kerov S.V. Asymptotics of the largest and the typical dimensions of the irreducible representations of a symmetric group. Funktsional. Anal. i Prilozhen. 19 1 (1985) 25-36
    • (1985) Funktsional. Anal. i Prilozhen. , vol.19 , Issue.1 , pp. 25-36
    • Vershik, A.M.1    Kerov, S.V.2
  • 40
    • 0035627643 scopus 로고    scopus 로고
    • Matrix integrals and geometry of spinors
    • van de Leur J.W. Matrix integrals and geometry of spinors. J. Nonlinear Math. Phys. 8 (2001) 288-311
    • (2001) J. Nonlinear Math. Phys. , vol.8 , pp. 288-311
    • van de Leur, J.W.1
  • 41
    • 0034335592 scopus 로고    scopus 로고
    • Soliton solutions of integrable hierarchies and Coulomb plasmas
    • Loutsenko I.M., and Spiridonov V. Soliton solutions of integrable hierarchies and Coulomb plasmas. J. Stat. Phys. 99 (2000) 751
    • (2000) J. Stat. Phys. , vol.99 , pp. 751
    • Loutsenko, I.M.1    Spiridonov, V.2
  • 48
    • 0038806289 scopus 로고    scopus 로고
    • Correlation function of Schur process with application to local geometry of a random 3-dimensional Young diagram
    • mathCO/0503508
    • Okounkov A., and Reshetikhin N. Correlation function of Schur process with application to local geometry of a random 3-dimensional Young diagram. J. Amer. Math. Soc. 16 (2003) 581-603. mathCO/0503508
    • (2003) J. Amer. Math. Soc. , vol.16 , pp. 581-603
    • Okounkov, A.1    Reshetikhin, N.2
  • 50
    • 32544432996 scopus 로고    scopus 로고
    • Hypergeometric functions as infinite-soliton Tau function
    • *) as ∞-soliton τ-function in T variables. nonlin.SI/0305001
    • *) as ∞-soliton τ-function in T variables. nonlin.SI/0305001
    • (2006) Theoret. and Math. Phys. , vol.146 , Issue.2 , pp. 183-206
    • Orlov, A.Yu.1
  • 53
    • 0035872958 scopus 로고    scopus 로고
    • Multivariate hypergeometric functions as tau functions of Toda lattice and Kadomtsev-Petviashvili equation
    • Orlov A.Yu., and Scherbin D.M. Multivariate hypergeometric functions as tau functions of Toda lattice and Kadomtsev-Petviashvili equation. Physics D 152-153 (2001) 51-56
    • (2001) Physics , vol.D 152-153 , pp. 51-56
    • Orlov, A.Yu.1    Scherbin, D.M.2
  • 54
    • 22744440816 scopus 로고    scopus 로고
    • Schur function expansion for normal matrix model and associated discrete matrix models
    • (More completed version in math-ph/0501017 )
    • Orlov A.Yu., and Shiota T. Schur function expansion for normal matrix model and associated discrete matrix models. Phys. Lett. A 343 (2005) 384-396. (More completed version in math-ph/0501017 )
    • (2005) Phys. Lett. A , vol.343 , pp. 384-396
    • Orlov, A.Yu.1    Shiota, T.2
  • 56
    • 0041416165 scopus 로고    scopus 로고
    • Exact nonstationary probabilities in the asymmetric exclusion process on a ring
    • Priezzhev V.B. Exact nonstationary probabilities in the asymmetric exclusion process on a ring. Phys. Rev. Lett. 19 (2003) 050601-1-050601-4
    • (2003) Phys. Rev. Lett. , vol.19
    • Priezzhev, V.B.1
  • 60
    • 0001361390 scopus 로고
    • Initial value problem for the Toda lattice hierarchy
    • Takasaki K. Initial value problem for the Toda lattice hierarchy. Adv. Stud. Pure Math. 4 (1984) 139-163
    • (1984) Adv. Stud. Pure Math. , vol.4 , pp. 139-163
    • Takasaki, K.1
  • 61
    • 0040650400 scopus 로고
    • Representation theoretical meaning of initial value problem for the Toda lattice hierarchy I
    • Takebe T. Representation theoretical meaning of initial value problem for the Toda lattice hierarchy I. Lett. Math. Phys. 21 (1991) 77-84
    • (1991) Lett. Math. Phys. , vol.21 , pp. 77-84
    • Takebe, T.1
  • 62
    • 85007994930 scopus 로고
    • Representation theoretical meaning of initial value problem for the Toda lattice hierarchy II
    • Takebe T. Representation theoretical meaning of initial value problem for the Toda lattice hierarchy II. Publ. Res. Inst. Math. Sci. Kyoto Univ. 27 (1991) 491-503
    • (1991) Publ. Res. Inst. Math. Sci. Kyoto Univ. , vol.27 , pp. 491-503
    • Takebe, T.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.