论文标题
提取子集最大化能力和随机步行的折叠
Extracting subsets maximizing capacity and Folding of Random Walks
论文作者
论文摘要
我们证明，在任何有限的$ \ mathbb z^d $的有限集中，带有$ d \ ge 3 $，有一个子集的容量和音量都与初始集合的容量相同。作为一个应用程序，我们获得了{\ it均匀覆盖}的概率的估计值，并在最佳假设下表征了一些{\ it折叠}事件。例如，知道一个空间区域具有一个随机步行的空间{\ IT非典型高职业密度}，我们表明这个随机区域很可能像球一样
We prove that in any finite set of $\mathbb Z^d$ with $d\ge 3$, there is a subset whose capacity and volume are both of the same order as the capacity of the initial set. As an application we obtain estimates on the probability of {\it covering uniformly} a finite set, and characterize some {\it folding} events, under optimal hypotheses. For instance, knowing that a region of space has an {\it atypically high occupation density} by some random walk, we show that this random region is most likely ball-like
