论文标题
通过随机讲述断开点的点过多的偏差
Excess deviations for points disconnected by random interlacements
论文作者
论文摘要
我们考虑在$ \ mathbb {z}^d $，$ d \ ge 3 $上的随机讲述，当它们的空置设置处于强烈的渗透状态时。给定一个以原点为中心的大盒子，我们建立了一个渐近上限，该盒子的衰减速率是该盒中包含过量分数的$ν$点的衰减率，这些点是由从同心双重大小的同心盒边界的随机中间隔离中断开的。作为一个应用程序，我们表明，当$ν$不太大时，这种渐近上限与作者先前作品中衍生得出的渐近下限匹配，并且衰减的指数速率受到连续体的某些变异问题的控制，涉及涉及随机交流的空置集合的渗透功能。
We consider random interlacements on $ \mathbb{Z}^d$, $d \ge 3$, when their vacant set is in a strongly percolative regime. Given a large box centered at the origin, we establish an asymptotic upper bound on the exponential rate of decay of the probability that the box contains an excessive fraction $ν$ of points that are disconnected by random interlacements from the boundary of a concentric box of double size. As an application we show that when $ν$ is not too large, this asymptotic upper bound matches the asymptotic lower bound derived in a previous work of the author, and the exponential rate of decay is governed by a certain variational problem in the continuum which involves the percolation function of the vacant set of random interlacements.
