Crossover to the KPZ equation

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 $a{n}^{2-\gamma }$ ($a,\gamma >0$) 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.

Published by Annales Henri Poincare Volume 13, Number 4 (2012), 813-826

References in corpus (8)

• Probability Distribution of the Free Energy of the Continuum Directed Random Polymer in 1+1 dimensions
• The one-dimensional KPZ equation: an exact solution and its universality
• Asymptotics in ASEP with Step Initial Condition
• The crossover regime for the weakly asymmetric simple exclusion process
• Total Current Fluctuations in ASEP
• Cumulants of the current in the weakly asymmetric exclusion process
• Universality of KPZ equation
• Scaling exponent for the Hopf-Cole solution of KPZ/Stochastic Burgers

Cited by in corpus (12)

• Nonlinear fluctuations of weakly asymmetric interacting particle systems
• A stochastic Burgers equation from a class of microscopic interactions
• Weakly asymmetric bridges and the KPZ equation
• Crossover to the stochastic Burgers equation for the WASEP with a slow bond
• Universality of deterministic KPZ
• Local KPZ behavior under arbitrary scaling limits
• The Einstein relation for the KPZ equation
• Stochastic PDE limit of the dynamic ASEP
• On energy solutions to stochastic Burgers equation
• Combined use of mixed and hybrid finite elements method with domain decomposition and spectral methods for a study of renormalization for the KPZ model
• Characterization of Gradient Condition for Asymmetric Partial Exclusion Processes and Their Scaling Limits
• A Microscopic Derivation Of Coupled Spde's With A Kpz Flavor