Fluctuations of the solutions to the KPZ equation in dimensions three and higher

2018/12/14 by Dunlap, Alexander, Gu, Yu, Ryzhik, Lenya +1 · 1 citation
#FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR)

paper · doi:10.48550/arxiv.1812.05768

Abstract

We prove, using probabilistic techniques and analysis on the Wiener space, that the large scale fluctuations of the KPZ equation in d≥ 3 with a small coupling constant, driven by a white in time and colored in space noise, are given by the Edwards-Wilkinson model. This gives an alternative proof, that avoids perturbation expansions, to the results of Magnen and Unterberger \citemagnen2017diffusive.

Cited by

• Edwards-Wilkinson limit for a stochastic advection-diffusion PDE

Related

• Gaussian fluctuations from the 2D KPZ equation
• Fluctuations of a nonlinear stochastic heat equation in dimensions three and higher
• The two-dimensional KPZ equation in the entire subcritical regime
• Scaling limit of the KPZ equation with non-integrable spatial correlations
• The scaling limit of the KPZ equation in space dimension 3 and higher