论文标题
随机电导模型的不均匀抛物线方程和应用
Non-uniformly parabolic equations and applications to the random conductance model
论文作者
论文摘要
我们研究了与$ \ mathbb z^d $上的随机电导模型相关的线性，非均匀抛物线有限差异算子的局部规则性特性。特别是，我们提供振荡衰减，假设电导的某些总和性及其逆，从而改善了该方向的最新结果。作为应用程序，我们在随机归化和无限环境中为随机行走提供了局部限制定理。
We study local regularity properties of linear, non-uniformly parabolic finite-difference operators in divergence form related to the random conductance model on $\mathbb Z^d$. In particular, we provide an oscillation decay assuming only certain summability properties of the conductances and their inverse, thus improving recent results in that direction. As an application, we provide a local limit theorem for the random walk in a random degenerate and unbounded environment.
