论文标题
在大偏差和随机讲述的交点上
On large deviations and intersection of random interlacements
论文作者
论文摘要
我们研究了$ \ mathbb {z}^d $与$ d \ geq 3 $上的随机讲述，并在宏观盒中设置的插件的容量比盒子小得多的概率得出了较大的偏差率。作为应用程序，我们获得了较大的偏差速率，因为两个独立的中插条在宏观框中具有空的交叉点的概率。我们还证明，在此事件上进行条件，其中一个在容量方面将很少。该结果是熵排斥现象的一个例子，用于随机中间的插条。
We investigate random interlacements on $\mathbb{Z}^d$ with $d \geq 3$, and derive the large deviation rate for the probability that the capacity of the interlacement set in a macroscopic box is much smaller than that of the box. As an application, we obtain the large deviation rate for the probability that two independent interlacements have empty intersections in a macroscopic box. We also prove that conditioning on this event, one of them will be sparse in the box in terms of capacity. This result is an example of the entropic repulsion phenomenon for random interlacements.
