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October, 2015 Disconnection and level-set percolation for the Gaussian free field
Alain-Sol SZNITMAN
J. Math. Soc. Japan 67(4): 1801-1843 (October, 2015). DOI: 10.2969/jmsj/06741801

Abstract

We study the level-set percolation of the Gaussian free field on $\mathbb Z^d$, $d \ge 3$. We consider a level $\alpha$ such that the excursion-set of the Gaussian free field above $\alpha$ percolates. We derive large deviation estimates on the probability that the excursion-set of the Gaussian free field below the level $\alpha$ disconnects a box of large side-length from the boundary of a larger homothetic box. It remains an open question whether our asymptotic upper and lower bounds are matching. With the help of a recent work of Lupu [21], we are able to infer some asymptotic upper bounds for similar disconnection problems by random interlacements, or by simple random walk.

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Alain-Sol SZNITMAN. "Disconnection and level-set percolation for the Gaussian free field." J. Math. Soc. Japan 67 (4) 1801 - 1843, October, 2015. https://doi.org/10.2969/jmsj/06741801

Information

Published: October, 2015
First available in Project Euclid: 27 October 2015

zbMATH: 1337.60246
MathSciNet: MR3417515
Digital Object Identifier: 10.2969/jmsj/06741801

Subjects:
Primary: 60F10, 60G15, 60K35, 82B43

Rights: Copyright © 2015 Mathematical Society of Japan

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Vol.67 • No. 4 • October, 2015
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