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On the transience of random interlacements. (English) Zbl 1231.60115

Summary: 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 A.-S. Sznitman [Ann. Math. (2) 171, No. 3, 2039–2087 (2010; Zbl 1202.60160)]. We prove that for any \(u>0\), almost surely, the random interlacement graph is transient.

MSC:

60K35 Interacting random processes; statistical mechanics type models; percolation theory
82B43 Percolation
82C41 Dynamics of random walks, random surfaces, lattice animals, etc. in time-dependent statistical mechanics

Citations:

Zbl 1202.60160
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