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arXiv · 2107.11583

Asymptotic expansion of the annealed Green's function and its derivatives

Matthias Keller·Marius Lemm
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Abstract

We consider random elliptic equations in dimension $d\geq 3$ at small ellipticity contrast. We derive the large-distance asymptotic expansion of the annealed Green's function up to order $4$ in $d=3$ and up to order $d+2$ for $d\geq 4$. We also derive asymptotic expansions of its derivatives. The obtained precision lies far beyond what is established in prior results in stochastic homogenization theory. Our proof builds on a recent breakthrough in perturbative stochastic homogenization by Bourgain in a refined version shown by Kim and the second author, and on Fourier-analytic techniques of Uchiyama.

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Matthias Keller, Marius Lemm. 2021-07-24. Asymptotic expansion of the annealed Green's function and its derivatives. https://arxiv.org/abs/2107.11583

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