## Electronic Journal of Probability

### A lower bound for disconnection by random interlacements

#### Abstract

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

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

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

https://projecteuclid.org/euclid.ejp/1465065659

Digital Object Identifier
doi:10.1214/EJP.v19-3067

Mathematical Reviews number (MathSciNet)
MR3164770

Zentralblatt MATH identifier
1355.60035

Rights

#### Citation

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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