On the transience of random interlacements

Abstract

We consider the interlacement Poisson point process on the space of doubly-infinite $\mathbb{Z}^d$-valued trajectories modulo time-shift, tending to infinity at positive and negative infinite times. The set of vertices and edges visited by at least one of these trajectories is the graph induced by the random interlacements at level $u$ of Sznitman(2010). We prove that for any $u > 0$, almost surely, the random interlacement graph is transient.