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 an2−γ (a,γ>0) and it occurs at
γ=1/2. We show that the density field is a solution of an
Ornstein-Uhlenbeck equation if γ∈(1/2,1], while for γ=1/2 it is
an energy solution of the KPZ equation. The corresponding crossover for the
current of particles is readily obtained.Comment: Published by Annales Henri Poincare Volume 13, Number 4 (2012),
813-82