CURRENT FLUCTUATIONS FOR TASEP: A PROOF OF THE PRAHOFER-SPOHN CONJECTURE

• 成果类型: Article
• 署名作者: Ben Arous, Gerard; Corwin, Ivan
• 署名单位: New York University
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/10-AOP550
• 发表日期: 2011
• 页码: 104-138
• 关键词: asymmetric simple exclusion; sample covariance matrices; polynuclear growth-model; limiting distributions; shock fluctuations; EXTERNAL SOURCES; formulas; particle; profile; asep

摘要

We consider the family of two-sided Bernoulli initial conditions for TASEP which, as the left and right densities (rho-, rho+) are varied, give rise to shock waves and rarefaction fans-the two phenomena which are typical to TASEP. We provide a proof of Conjecture 7.1 of [Progr. Probab. 51 (2002) 185-204] which characterizes the order of and scaling functions for the fluctuations of the height function of two-sided TASEP in terms of the two densities rho-, rho+ and the speed y around which the height is observed. In proving this theorem for TASEP, we also prove a fluctuation theorem for a class of corner growth processes with external sources, or equivalently for the last passage time in a directed last passage percolation model with two-sided boundary conditions: rho- and 1 - rho+. We provide a complete characterization of the order of and the scaling functions for the fluctuations of this model's last passage time L(N, M) as a function of three parameters: the two boundary/source rates rho- and 1 - rho+, and the scaling ratio gamma(2) = M/N. The proof of this theorem draws on the results of [Comm. Math. Phys. 265 (2006) 1-44] and extensively on the work of [Ann. Probab. 33 (2005) 1643-1697] on finite rank perturbations of Wishart ensembles in random matrix theory.