The Annals of Probability

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

Gérard Ben Arous and Ivan Corwin

Full-text: Open access

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=MN. 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.

Article information

Source
Ann. Probab. Volume 39, Number 1 (2011), 104-138.

Dates
First available: 3 December 2010

Permanent link to this document
http://projecteuclid.org/euclid.aop/1291388298

Digital Object Identifier
doi:10.1214/10-AOP550

Mathematical Reviews number (MathSciNet)
MR2778798

Subjects
Primary: 82C22: Interacting particle systems [See also 60K35] 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]

Keywords
Asymmetric simple exclusion process interacting particle systems last passage percolation

Citation

Ben Arous, Gérard; Corwin, Ivan. Current fluctuations for TASEP: A proof of the Prähofer–Spohn conjecture. The Annals of Probability 39 (2011), no. 1, 104--138. doi:10.1214/10-AOP550. http://projecteuclid.org/euclid.aop/1291388298.


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