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May 2020 Percolation for level-sets of Gaussian free fields on metric graphs
Jian Ding, Mateo Wirth
Ann. Probab. 48(3): 1411-1435 (May 2020). DOI: 10.1214/19-AOP1397

Abstract

We study level-set percolation for Gaussian free fields on metric graphs. In two dimensions, we give an upper bound on the chemical distance between the two boundaries of a macroscopic annulus. Our bound holds with high probability conditioned on connectivity and is sharp up to a poly-logarithmic factor with an exponent of one-quarter. This substantially improves a previous result by Li and the first author. In three dimensions and higher, we provide rather precise estimates of percolation probabilities in different regimes which altogether describe a sharp phase transition.

Citation

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Jian Ding. Mateo Wirth. "Percolation for level-sets of Gaussian free fields on metric graphs." Ann. Probab. 48 (3) 1411 - 1435, May 2020. https://doi.org/10.1214/19-AOP1397

Information

Received: 1 October 2018; Revised: 1 April 2019; Published: May 2020
First available in Project Euclid: 17 June 2020

zbMATH: 07226365
MathSciNet: MR4112719
Digital Object Identifier: 10.1214/19-AOP1397

Subjects:
Primary: 60G60, 60K35

Rights: Copyright © 2020 Institute of Mathematical Statistics

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Vol.48 • No. 3 • May 2020
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