由随机交错断开的点的过量偏差
Excess deviations for points disconnected by random interlacements
摘要：
我们考虑随机交错上的$ \mathbb{Z}^d$，$d \ge 3$，当他们的空集是在一个强并行的制度。给定一个以原点为中心的大盒子，我们建立了一个渐近上界的概率的指数衰减率，该盒子包含一个多余的分数$ν$的点，从一个同心框的边界随机交错断开。作为一个应用程序，我们表明，当$ν$是不是太大，这个渐近上界匹配的渐近下界在作者以前的工作中得出的，和指数衰减率是由一定的变分问题在连续，其中涉及的随机交错的空集的渗流函数。
英文摘要：
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.
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