Fluctuations of Parabolic Equations with Large Random Potentials

Abstract

In this paper, we present a fluctuation analysis of a type of parabolic equations with large, highly oscillatory, random potentials around the homogenization limit. With a Feynman-Kac representation, the Kipnis-Varadhan's method, and a quantitative martingale central limit theorem, we derive the asymptotic distribution of the rescaled error between heterogeneous and homogenized solutions under different assumptions in dimension $d\geq 3$. The results depend highly on whether a stationary corrector exits.