Exceptional points of discrete-time random walks in planar domains
Exceptional points of discrete-time random walks in planar domains
复制标题
平面域中离散时间随机游走的特异点
DOI：
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发表时间：
2019
影响因子：
1.4
通讯作者：
Sangchul Lee
中科院分区：
文献类型：
--
作者：
Y. Abe;M. Biskup;Sangchul Lee
给定有界连续区域$Dsubsetmathbb R^2 $的一系列格逼近$DNsubsetmathbb Z^2 $，其中$DN $外的顶点融合在一起成为一个边界顶点$varrho$，我们考虑$DNcup {varrho}$中的离散时间简单随机游动，其时间与期望覆盖时间成正比，并描述了厚，薄，光和避免点。我们表明，这些分布，一个空间依赖的对数正态因子，作为零平均刘维尔量子引力措施在$D$。并确定了异常点及其附近局部时位形的极限律。结果扩展了早期工作的前两个作者谁分析了连续时间问题的参数化的本地时间在$varrho$。一个新的唯一性结果，关于可分随机措施，特别是高斯乘性混沌，推导出的一部分的证据。
Given a sequence of lattice approximations $D_Nsubsetmathbb Z^2$ of a bounded continuum domain $Dsubsetmathbb R^2$ with the vertices outside $D_N$ fused together into one boundary vertex $varrho$, we consider discrete-time simple random walks in $D_Ncup{varrho}$ run for a time proportional to the expected cover time and describe the scaling limit of the exceptional level sets of the thick, thin, light and avoided points. We show that these are distributed, up a spatially-dependent log-normal factor, as the zero-average Liouville Quantum Gravity measures in $D$. The limit law of the local time configuration at, and nearby, the exceptional points is determined as well. The results extend earlier work by the first two authors who analyzed the continuous-time problem in the parametrization by the local time at $varrho$. A novel uniqueness result concerning divisible random measures and, in particular, Gaussian Multiplicative Chaos, is derived as part of the proofs.
影响因子：
2
作者：
Abe, Yoshihiro;Biskup, Marek
通讯作者：
Biskup, Marek