On the transience of random interlacements

2011/02/28 by Balázs Ráth, Artëm Sapozhnikov · 1 citation
Mathematics · #math.PR #msc:60K35

paper · pdf

published as Electronic communications in probability 16 (2011), 379-391

arxiv created 2011/07/17 · arxiv updated 2011/07/19

Abstract

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.

Citations

• Vacant Set of Random Interlacements and Percolation

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