期刊
STOCHASTICS AND PARTIAL DIFFERENTIAL EQUATIONS-ANALYSIS AND COMPUTATIONS
卷 7, 期 2, 页码 240-296出版社
SPRINGER
DOI: 10.1007/s40072-018-0127-8
关键词
Random conductance model; Berry-Esseen theorem; Quantitative homogenization; Corrector; 60K37; 60F05; 35B27; 35K65
资金
- German Research Foundation in the Collaborative Research Center 1060 The Mathematics of Emergent Effects, Bonn
- DFG
We study the random conductance model on the lattice Zd, i.e. we consider a linear, finite-difference, divergence-form operator with random coefficients and the associated random walk under random conductances. We allow the conductances to be unbounded and degenerate elliptic, but they need to satisfy a strong moment condition and a quantified ergodicity assumption in form of a spectral gap estimate. As a main result we obtain in dimension d3 quantitative central limit theorems for the random walk in form of a Berry-Esseen estimate with speed t-15+epsilon for d4 and t-110+epsilon for d=3. Additionally, in the uniformly elliptic case in low dimensions d=2,3 we improve the rate in a quantitative Berry-Esseen theorem recently obtained by Mourrat. As a central analytic ingredient, for d3 we establish near-optimal decay estimates on the semigroup associated with the environment process. These estimates also play a central role in quantitative stochastic homogenization and extend some recent results by Gloria, Otto and the second author to the degenerate elliptic case.
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