Current fluctuations for TASEP: A proof of the Prähofer-Spohn conjecture

Gérard Ben Arous, Ivan Corwin

Research output: Contribution to journalArticle

Abstract

We consider the family of two-sided Bernoulli initial conditions for TASEP which, as the left and right densities (ρ-,ρ+) 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 ρ-,ρ+ 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: ρ- and 1-ρ+. 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 ρ- and 1 - ρ+, and the scaling ratio γ2 = 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.

Original languageEnglish (US)
Pages (from-to)104-138
Number of pages35
JournalAnnals of Probability
Volume39
Issue number1
DOIs
StatePublished - Jan 2011

Keywords

  • Asymmetric simple exclusion process
  • Interacting particle systems
  • Last passage percolation

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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