Electronic Journal of Probability

A lower bound for disconnection by random interlacements

Xinyi Li and Alain-Sol Sznitman

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We consider the vacant set of random interlacements on $\mathbb{Z}^d$, with $d$ bigger or equal to 3, in the percolative regime. Motivated by the large deviation principles obtained in our recent work arXiv:1304.7477, we investigate the asymptotic behavior of the probability that a large body gets disconnected from infinity by the random interlacements. We derive an asymptotic lower bound, which brings into play tilted interlacements, and relates the problem to some of the large deviations of the occupation-time profile considered in arXiv:1304.7477.

Article information

Electron. J. Probab., Volume 19 (2014), paper no. 17, 26 pp.

Accepted: 28 January 2014
First available in Project Euclid: 4 June 2016

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Zentralblatt MATH identifier

Primary: 60F10: Large deviations
Secondary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43] 60J27: Continuous-time Markov processes on discrete state spaces

random interlacements disconnection large deviations

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Li, Xinyi; Sznitman, Alain-Sol. A lower bound for disconnection by random interlacements. Electron. J. Probab. 19 (2014), paper no. 17, 26 pp. doi:10.1214/EJP.v19-3067. https://projecteuclid.org/euclid.ejp/1465065659

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