Fluctuations of parabolic equations with large random potentials
Tóm tắt
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
$$d\ge 3$$
. The results depend highly on whether a stationary corrector exits.
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