Abstract
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-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 \({\gamma\in(1/2,1]}\) , 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.
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Communicated by Bernard Nienhuis.
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Gonçalves, P., Jara, M. Crossover to the KPZ Equation. Ann. Henri Poincaré 13, 813–826 (2012). https://doi.org/10.1007/s00023-011-0147-7
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DOI: https://doi.org/10.1007/s00023-011-0147-7