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

Ráth, Balázs; Sapozhnikov, Artëm

Electron. Commun. Probab. 16, 379-391 (2011).

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

Keywords:

random interlacement; random walk; resistance; intersection of random walks; capacity

Citations:

Zbl 1202.60160