Current fluctuations for TASEP

A proof of the Prähofer-Spohn conjecture

Gerard 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

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Current Fluctuations
Passage Time
Scaling Function
Fluctuations
Fluctuation Theorem
Random Matrix Theory
Growth Process
Finite Rank
Theorem
Bernoulli
Shock Waves
Ensemble
Initial conditions
Scaling
Perturbation
Boundary conditions
Model
Class
Family

Keywords

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

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Cite this

Current fluctuations for TASEP : A proof of the Prähofer-Spohn conjecture. / Ben Arous, Gerard; Corwin, Ivan.

In: Annals of Probability, Vol. 39, No. 1, 01.2011, p. 104-138.

Research output: Contribution to journalArticle

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