Fluctuations of Parabolic Equations with Large Random Potentials

2013/12/01 by Yu Gu, Gu, Yu, Guillaume Bal +1
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Probability (math.PR) #Stochastic processes and statistical mechanics #math.AP #math.PR

paper · pdf · doi:10.48550/arxiv.1312.0238

44 pages; reorganized the structure and extended the results; to appear in SPDE: Analysis and Computations

openalex publication_date 2013/12/01 · arxiv created 2014/09/28 · arxiv updated 2014/09/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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≥ 3. The results depend highly on whether a stationary corrector exits.

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