Fluctuations of Parabolic Equations with Large Random Potentials

Yu Gu; Guillaume Bal

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arXiv · 1312.0238

Fluctuations of Parabolic Equations with Large Random Potentials

Yu Gu·Guillaume Bal

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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.

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Yu Gu, Guillaume Bal. 2014-09-28. Fluctuations of Parabolic Equations with Large Random Potentials. https://arxiv.org/abs/1312.0238

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