Electronic Communications in Probability

On the transience of random interlacements

Balazs Rath and Artem Sapozhnikov

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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

Permanent link to this document
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

Subjects
Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]
Secondary: 82B43: Percolation [See also 60K35]

Keywords
Random interlacement transience random walk resistance intersection of random walks capacity

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

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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