We establish a quenched local central limit theorem for the dynamic random conductance model on \({\mathbb {Z}}^d\) only assuming ergodicity with respect to space-time shifts and a moment condition. As a key analytic ingredient we show Hölder continuity estimates for solutions to the heat equation for discrete finite difference operators in divergence form with time-dependent degenerate weights. The proof is based on De Giorgi’s iteration technique. In addition, we also derive a quenched local central limit theorem for the static random conductance model on a class of random graphs with degenerate ergodic weights.

中文翻译：

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时间依赖的遍历简并权重中随机游动的淬灭局部极限定理

我们仅在关于时空移位和力矩条件假设为遍历性的情况下，针对\（{\ mathbb {Z}} ^ d \）上的动态随机电导模型建立了一个淬灭的局部中心极限定理。作为关键的分析成分，我们显示了离散形式的有限差分算子的热方程解的Hölder连续性估计，其离散形式具有随时间变化的简并权重。该证明基于De Giorgi的迭代技术。此外，我们还针对一类具有退化遍历权重的随机图，针对静态随机电导模型导出了一个淬灭的局部中心极限定理。