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2016 Coupling and an application to level-set percolation of the Gaussian free field
Alain-Sol Sznitman
Electron. J. Probab. 21: 1-26 (2016). DOI: 10.1214/16-EJP4563

Abstract

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.

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Alain-Sol Sznitman. "Coupling and an application to level-set percolation of the Gaussian free field." Electron. J. Probab. 21 1 - 26, 2016. https://doi.org/10.1214/16-EJP4563

Information

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

zbMATH: 1336.60194
MathSciNet: MR3492939
Digital Object Identifier: 10.1214/16-EJP4563

Subjects:
Primary: 60G15, 60J27, 60J80, 60K35, 82B43

JOURNAL ARTICLE
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Vol.21 • 2016
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