论文标题
在退化动态随机环境中进行一维随机步行的不变性原理
An invariance principle for one-dimensional random walks in degenerate dynamical random environments
论文作者
论文摘要
我们研究了由时间依赖的最近邻邻电导的样本驱动的整数上的随机步行，这些电导量是有界的，但可以随着时间的间隔而消失。假设仅在时空移动下进行电导法的终身性，并且对在给定边缘积聚单位电导的时间的时刻假设，我们证明，步行量表在空间和时间的扩散尺度下，到达非分类的布朗尼运动。实现环境。该结论尤其适用于一维动力学渗透的随机步行，但要受到相当通用的固定式边缘动力学的影响。
We study random walks on the integers driven by a sample of time-dependent nearest-neighbor conductances that are bounded but are permitted to vanish over time intervals of positive Lebesgue-length. Assuming only ergodicity of the conductance law under space-time shifts and a moment assumption on the time to accumulate a unit conductance over a given edge, we prove that the walk scales, under a diffusive scaling of space and time, to a non-degenerate Brownian motion for a.e. realization of the environment. The conclusion particularly applies to random walks on one-dimensional dynamical percolation subject to fairly general stationary edge-flip dynamics.
