论文标题
淬灭局部限制定理，以在时间依赖的千古归化重量中随机步行
Quenched local limit theorem for random walks among time-dependent ergodic degenerate weights
论文作者
论文摘要
我们在$ \ mathbb {z}^d $上为动态随机电导模型建立了一个淬火的局部中央限制定理，仅假设相对于时空偏移和力矩条件，就假设存在千古。作为关键的分析成分，我们显示了Hölder的连续性估计值，用于以时间依赖性的退化权重以分散形式的离散有限差算子的溶液。证明是基于De Giorgi的迭代技术。此外，我们还为具有退化的厄乳态权重的一类随机图上的静态随机电导模型得出了猝灭的局部中心极限定理。
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.
