2009/05/31 by Gérard Ben Arous, Ivan Corwin · 2 citations
Mathematics · Physics and Astronomy · #Navier-Stokes equation solutions #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #math-ph #math.MP #math.PR
paper · pdf · doi:10.1214/10-aop550
published as Annals of Probability 2011, Vol. 39, No. 1, 104-138 · Published in at http://dx.doi.org/10.1214/10-AOP550 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)
openalex publication_date 2010/12/03 · arxiv created 2010/12/07 · arxiv updated 2011/03/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
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.