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2015 High-dimensional asymptotics for percolation of Gaussian free field level sets
Alexander Drewitz, Pierre-Francois Rodriguez
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Electron. J. Probab. 20: 1-39 (2015). DOI: 10.1214/EJP.v20-3416

Abstract

We consider the Gaussian free field on $Z^d$, $d\geq3$, and prove that the critical density for percolation of its level sets behaves like $1/d^{1+o(1)}$ as $d$ tends to infinity. Our proof gives the principal asymptotic behavior of the corresponding critical level $h_*(d)$. Moreover, it shows that a related parameter $h_{**}(d)$ introduced by Rodriguez and Sznitman in [23] is in fact asymptotically equivalent to $h_*(d)$.

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Alexander Drewitz. Pierre-Francois Rodriguez. "High-dimensional asymptotics for percolation of Gaussian free field level sets." Electron. J. Probab. 20 1 - 39, 2015. https://doi.org/10.1214/EJP.v20-3416

Information

Accepted: 25 April 2015; Published: 2015
First available in Project Euclid: 4 June 2016

zbMATH: 1321.60207
MathSciNet: MR3339867
Digital Object Identifier: 10.1214/EJP.v20-3416

Subjects:
Primary: 60G15
Secondary: 60G60, 60K35, 82B43

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