Universality of slow decorrelation in KPZ growth

Annales de l'institut Henri Poincare (B) Probability and Statistics

Volumn 48, Issue 1, 2012, Pages 134-150

  Corwin, Ivan ^a   Ferrari, Patrik L ^b   Péché, Sandrine ^c,d  

^a NEW YORK UNIVERSITY   (United States)

^b UNIVERSITY OF BONN   (Germany)

^c INSTITUT FOURIER   (France)

^d UNIVERSITÉ PARIS DESCARTES   (France)

Author keywords

Asymmetric simple exclusion process; Directed polymers; Interacting particle systems; KPZ; Last passage percolation

Indexed keywords

EID: 84856286981     PISSN: 02460203     EISSN: None     Source Type: Journal    
DOI: 10.1214/11-AIHP440     Document Type: Article

References (42)

1. G. Amir, I. Corwin and J. Quastel. Probability distribution of the free energy of the continuum directed random polymer in 1 + 1 dimensions. Comm. Pure Appl. Math. 64 (2011) 466-537. MR2796514
2. J. Baik. Painlevé formulas of the limiting distributions for nonnull complex sample covariance matrices. Duke Math. J. 33 (2006) 205-235. MR2225691 (Pubitemid 43988241)
3. J. Baik, G. Ben Arous and S. Péché. Phase transition of the largest eigenvalue for nonnull complex sample covariance matrices. Ann. Probab. 33 (2005) 1643-1697. MR2165575 (Pubitemid 41560766)
4. J. Baik, P. L. Ferrari and S. Péché. Limit process of stationary TASEP near the characteristic line. Comm. Pure Appl. Math. 63 (2010) 1017-1070. MR2642384
5. J. Baik and E. Rains. Limiting distributions for a polynuclear growth model with external sources. J. Stat. Phys. 100 (2000) 523-541. MR1788477
6. G. Ben Arous and I. Corwin. Current fluctuations for TASEP: A proof of the Prähofer-Spohn conjecture. Ann. Probab. 39 (2011) 104-138. MR2778798
7. L. Bertini and G. Giacomin. Stochastic burgers and KPZ equations from particle systems. Comm. Math. Phys. 183 (1997) 571-607. MR1462228 (Pubitemid 127355687)
8. 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. MR2438811
9. 1 process. Int. Math. Res. Papers1 (2007) rpm002. MR2334008
10. 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. MR2363389
11. 2 processes and TASEP fluctuations. Comm. Pure Appl. Math. 61 (2008) 1603-1629. MR2444377
12. A. Borodin, P. L. Ferrari and T. Sasamoto. Large time asymptotics of growth models on space-like paths II: PNG and parallel TASEP. Comm. Math. Phys. 283 (2008) 417-449. MR2430639
13. A. Borodin, P. L. Ferrari and T. Sasamoto. Two speed TASEP. J. Stat. Phys. 137 (2009) 936-977. MR2570757
14. 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. MR2415103
15. I. Corwin, P. L. Ferrari and S. Péché. Limit processes for TASEP with shocks and rarefaction fans. J. Stat. Phys. 140 (2010) 232-267. MR2659279
16. I. Corwin and J. Quastel. Universal distribution of fluctuations at the edge of the rarefaction fan. Available at arXiv:1006.1338.
17. I. Corwin and J. Quastel. Renormalization fixed point of the KPZ universality class. Unpublished manuscript. Available at arXiv:1103.3422.
18. L. C. Evans. Partial Differential Equations, 2nd edition. Grad. Stud. Math. 19. Amer. Math. Soc., Providence, RI, 2010.
19. P. L. Ferrari. Slow decorrelations in KPZ growth. J. Stat. Mech. Theory Exp. 2008 (2008) P07022.
20. P. L. Ferrari. From interacting particle systems to random matrices. J. Stat. Mech. Theory Exp. 2010 (2010) P10016. MR2800495
21. T. Imamura and T. Sasamoto. Fluctuations of the one-dimensional polynuclear growth model with external sources. Nuclear Phys. B699 (2004) 503-544. MR2098552 (Pubitemid 39319594)
22. T. Imamura and T. Sasamoto. Dynamical properties of a tagged particle in the totally asymmetric simple exclusion process with the step-type initial condition. J. Stat. Phys. 128 (2007) 799-846. MR2344715
23. K. Johansson. Shape fluctuations and random matrices. Comm. Math. Phys. 209 (2000) 437-476. MR1737991
24. K. Johansson. Discrete polynuclear growth and determinantal processes. Comm. Math. Phys. 242 (2003) 277-329. MR2018275 (Pubitemid 37417719)
25. H. Kallabis and J. Krug. Persistence of Kardar-Parisi-Zhang interfaces. Europhys. Lett. 45 (1999) 20-25.
26. M. Kardar, G. Parisi and Y. C. Zhang. Dynamic scaling of growth interfaces. Phys. Rev. Lett. 56 (1986) 889-892.
27. J. Krug, H. Kallabis, S. N. Majumdar, S. J. Cornell, A. J. Bray and C. Sire. Persistence exponents for fluctuating interfaces. Phys. Rev. E56 (1997) 2702.
28. J. Krug and H. Spohn. Kinetic roughening of growning surfaces. In Solids Far From Equilibrium. C. Godrèche (Ed.). Cambridge Univ. Press, Cambridge, 1991.
29. T. M. Liggett. Stochastic Interacting Systems: Contact, Voter and Exclusion Processes. Springer, Berlin, 1999. MR1717346
30. T. M. Liggett. Interacting Particle Systems. Springer, Berlin, 2005. Reprint of 1985 original edition. MR2108619
31. M. Prähofer and H. Spohn. Current fluctuations for the totally asymmetric simple exclusion process. In In and Out of Equilibrium185-204. Progr. Probab. 51. Birkhäuser, Boston, MA, 2002. MR1901953
32. M. Prähofer and H. Spohn. Scale invariance of the PNG droplet and the Airy process. J. Stat. Phys. 108 (2002) 1071-1106. MR1933446 (Pubitemid 37133781)
33. H. Rost. Non-equilibrium behavior of a many particle process: Density profile and the local equilibrium. Z. Wahrsch. Verw. Gebiete58 (1981) 41-53. MR0635270
34. T. Sasamoto and H. Spohn. Universality of the one-dimensional KPZ equation. Phys. Rev. Lett. 104 (2010) 230602.
35. T. Seppälänen. Scaling for a one-dimensional directed polymer with constrained endpoints. Available at arXiv:0911.2446.
36. T. Seppäläinen. Hydrodyanamic scaling, convex duality and asymptotic shapes of growth models. Markov Process. Related Fields4 (1998) 1-26. MR1625007
37. C. Tracy and H. Widom. Level-spacing distributions and the Airy kernel. Comm. Math. Phys. 159 (1994) 151-174. MR1257246
38. C. Tracy and H. Widom. Integral formulas for the asymmetric simple exclusion process. Comm. Math. Phys. 279 (2008) 815-844. MR2386729
39. C. Tracy and H. Widom. A Fredholm determinant representation in ASEP. J. Stat. Phys. 132 (2008) 291-300. MR2415104
40. C. Tracy and H. Widom. Asymptotics in ASEP with step initial condition. Comm. Math. Phys. 290 (2009) 129-154. MR2520510
41. C. Tracy and H. Widom. Total current fluctuations in the asymmetric simple exclusion processes. J. Math. Phys. 50 (2009) 095204. MR2566884
42. C. Tracy and H. Widom. On ASEP with step Bernoulli initial condition. J. Stat. Phys. 137 (2009) 825-838. MR2570751