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تسجيل مستخدم جديدAsymptotic expansion of the annealed Greens function and its derivatives
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We consider random elliptic equations in dimension $dgeq 3$ at small ellipticity contrast. We derive the large-distance asymptotic expansion of the annealed Greens function up to order $4$ in $d=3$ and up to order $d+2$ for $dgeq 4$. 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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