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Berry-Esseen Theorem and Quantitative homogenization for the Random Conductance Model with degenerate Conductances. (arXiv:1706.09493v1 [math.PR])
来源于:arXiv
We study the random conductance model on the lattice $\mathbb{Z}^d$, 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 $d\geq
3$ quantitative central limit theorems for the random walk in form of a
Berry-Esseen estimate with speed $t^{-\frac 1 5+\varepsilon}$ for $d\geq 4$ and
$t^{-\frac{1}{10}+\varepsilon}$ for $d=3$. In addition, for $d\geq 3$ we show
near-optimal decay estimates on the semigroup associated with the environment
process, which plays a central role in quantitative stochastic homogenization.
This extends some recent results by Gloria, Otto and the second author to the
degenerate elliptic case. 查看全文>>