Crossover to the KPZ equation

Details Crossover to the KPZ equation Crossover to the KPZ equation

2010-04-15

arxiv.org/abs/1004.2726v3

Mathematics

Probability

13 pages, no figures, accepted for publication in the Annales Henri Poincar\'e

Scientific paper

We characterize the crossover regime to the KPZ equation for a class of one-dimensional weakly asymmetric exclusion processes. The crossover depends on the strength asymmetry $an^{2-\gamma}$ ($a,\gamma>0$) and it occurs at $\gamma=1/2$. We show that the density field is a solution of an Ornstein-Uhlenbeck equation if $\gamma\in(1/2,1]$, while for $\gamma=1/2$ it is an energy solution of the KPZ equation. The corresponding crossover for the current of particles is readily obtained.

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