On the internal distance in the interlacement set

Details On the internal distance in the interlacement set On the internal distance in the interlacement set

2011-11-16

arxiv.org/abs/1111.3979v2

Electronic Journal of Probability, Vol. 17, Article 29, p. 1-25 (2012)

Mathematics

Probability

26 pages, 3 figures

Scientific paper

10.1214/EJP.v17-1936

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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