Electronic Journal of Probability

Coupling and an application to level-set percolation of the Gaussian free field

Alain-Sol Sznitman

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In the present article we consider a general enough set-up and obtain a refinement of the coupling between the Gaussian free field and random interlacements recently constructed by Titus Lupu in [9]. We apply our results to level-set percolation of the Gaussian free field on a $(d+1)$-regular tree, when $d \ge 2$, and derive bounds on the critical value $h_*$. In particular, we show that $0 < h_* < \sqrt{2u_*} $, where $u_*$ denotes the critical level for the percolation of the vacant set of random interlacements on a $(d+1)$-regular tree.

Article information

Electron. J. Probab., Volume 21 (2016), paper no. 35, 26 pp.

Received: 24 September 2015
Accepted: 2 March 2016
First available in Project Euclid: 22 April 2016

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Zentralblatt MATH identifier

Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43] 60G15: Gaussian processes 60J27: Continuous-time Markov processes on discrete state spaces 60J80: Branching processes (Galton-Watson, birth-and-death, etc.) 82B43: Percolation [See also 60K35]

Gaussian free field random interlacements coupling level-set percolation

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Sznitman, Alain-Sol. Coupling and an application to level-set percolation of the Gaussian free field. Electron. J. Probab. 21 (2016), paper no. 35, 26 pp. doi:10.1214/16-EJP4563. https://projecteuclid.org/euclid.ejp/1461332876

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