Electronic Communications in Probability

On the transience of random interlacements

Balazs Rath and Artem Sapozhnikov

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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

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

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

Random interlacement transience random walk resistance intersection of random walks capacity

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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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