Crossover distributions at the edge of the rarefaction fan

Details Crossover distributions at the edge of the rarefaction fan Crossover distributions at the edge of the rarefaction fan

2010-06-07

arxiv.org/abs/1006.1338v3

Mathematics

Probability

59 pages, 3 figures; updated Proposition 10 and proof

Scientific paper

We consider the weakly asymmetric limit of simple exclusion process with drift to the left, starting from step Bernoulli initial data with rho_-BM process. As an application, we prove moment and large deviation estimates for the equilibrium Hopf-Cole solution of KPZ. These bounds rely on the apparently new observation that the FKG inequality holds for the stochastic heat equation. Finally, via a Feynman-Kac path integral, the KPZ equation also governs the free energy of the continuum directed polymer, and thus our formula may also be interpreted in those terms.

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