Abstract
We study the average Green’s function of stochastic, uniformly elliptic operators of divergence form on \(Zd\mathbb {Z}^d\). When the randomness is independent and has small variance, we prove regularity of the Fourier transform of the self-energy. The proof relies on the Schur complement formula and the analysis of singular integral operators combined with a Steinhaus system.
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Funding
The J. Bourgain was partially supported by NSF Grants DMS-1301619.
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Bourgain, J. On a Homogenization Problem. J Stat Phys 172, 314–320 (2018). https://doi.org/10.1007/s10955-018-1981-5
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DOI: https://doi.org/10.1007/s10955-018-1981-5