A central limit theorem for the KPZ equation

Abstract

We consider the KPZ equation in one space dimension driven by a stationary centred space-time random field, which is sufficiently integrable and mixing, but not necessarily Gaussian. We show that, in the weakly asymmetric regime, the solution to this equation considered at a suitable large scale and in a suitable reference frame converges to the Hopf-Cole solution to the KPZ equation driven by space-time Gaussian white noise. While the limiting process depends only on the integrated variance of the driving field, the diverging constants appearing in the definition of the reference frame also depend on higher order moments.

58 pages

References in corpus (4)

• Probability Distribution of the Free Energy of the Continuum Directed Random Polymer in 1+1 dimensions
• KPZ equation limit of higher-spin exclusion processes
• Wick polynomials and time-evolution of cumulants
• Renormalization Group and Stochastic PDE's

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• Glauber dynamics of 2D Kac-Blume-Capel model and their stochastic PDE limits
• Moment bounds for SPDEs with non-Gaussian fields and application to the Wong-Zakai problem