On the internal distance in the interlacement set

Jiří Černý (University of Vienna)
Serguei Popov (University of Campinas UNICAMP)


We prove a shape theorem for the internal (graph) distance on the interlacement set $\mathcal{I}^u$ of the random interlacement model on $\mathbb Z^d$, $d\ge 3$. 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.

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Pages: 1-25

Publication Date: April 12, 2012

DOI: 10.1214/EJP.v17-1936


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