On the internal distance in the interlacement set

被引：19

作者：

Cerny, Jiri ^{[1
]}

Popov, Serguei ^{[2
]}

机构：

[1] Univ Vienna, A-1010 Vienna, Austria

[2] Univ Campinas UNICAMP, Campinas, SP, Brazil

来源：

ELECTRONIC JOURNAL OF PROBABILITY | 2012年 / 17卷

关键词：

Random interlacement; Internal distance; Shape theorem; Simple random walk; Capacity; PERCOLATION; THEOREM;

D O I：

10.1214/EJP.v17-1936

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We prove a shape theorem for the internal (graph) distance on the interlacement set I-u of the random interlacement model on Z(d), d >= 3. We provide large deviation estimates for the internal distance of distant points in this set, and use these estimates to study the internal distance on the range of a simple random walk on a discrete torus.

引用

页码：1 / 25

页数：25

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