## Electronic Communications in Probability

### 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.

#### Article information

Source
Electron. Commun. Probab., Volume 16 (2011), paper no. 35, 379-391.

Dates
Accepted: 7 July 2011
First available in Project Euclid: 7 June 2016

https://projecteuclid.org/euclid.ecp/1465261991

Digital Object Identifier
doi:10.1214/ECP.v16-1637

Mathematical Reviews number (MathSciNet)
MR2819660

Zentralblatt MATH identifier
1231.60115

Rights

#### Citation

Rath, Balazs; Sapozhnikov, Artem. On the transience of random interlacements. Electron. Commun. Probab. 16 (2011), paper no. 35, 379--391. doi:10.1214/ECP.v16-1637. https://projecteuclid.org/euclid.ecp/1465261991

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