The Annals of Probability
- Ann. Probab.
- Volume 39, Number 1 (2011), 104-138.
Current fluctuations for TASEP: A proof of the Prähofer–Spohn conjecture
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.
Ann. Probab. Volume 39, Number 1 (2011), 104-138.
First available in Project Euclid: 3 December 2010
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Ben Arous, Gérard; Corwin, Ivan. Current fluctuations for TASEP: A proof of the Prähofer–Spohn conjecture. Ann. Probab. 39 (2011), no. 1, 104--138. doi:10.1214/10-AOP550. https://projecteuclid.org/euclid.aop/1291388298