On the transience of random interlacements

Balázs Ráth, Artëm Sapozhnikov

Published 2011-02-23, updated 2011-07-17Version 2

We consider the interlacement Poisson point process on the space of doubly-infinite 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 arXiv:0704.2560. We prove that for any u>0, almost surely, the random interlacement graph is transient.