Percolation for the Finitary Random interlacements

Abstract

In this paper, we prove a phase transition in the connectivity of Finitary Random interlacements ${\mathcal{F}\mathcal{I}}^{u,T}$ in ${\mathbb{Z}}^d$, with respect to the average stopping time. For each $u>0$, with probability one ${\mathcal{F}\mathcal{I}}^{u,T}$ has no infinite connected component for all sufficiently small $T>0$, and a unique infinite connected component for all sufficiently large $T<\infty$. This answers a question of Bowen in the special case of ${\mathbb{Z}}^d$.

22 pages