Level-set percolation for the Gaussian free field on a transient tree

DOI10.1214/16-AIHP799zbMath1396.60099arXiv1606.02411OpenAlexW3105292261MaRDI QIDQ1635965

Alain-Sol Sznitman, Angelo Abächerli

Publication date: 1 June 2018

Published in: Annales de l'Institut Henri Poincaré. Probabilités et Statistiques (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1606.02411

zbMATH Keywords

random interlacementsGaussian free fieldlevel-set percolationtransient trees

Mathematics Subject Classification ID

Gaussian processes (60G15) Interacting random processes; statistical mechanics type models; percolation theory (60K35) Markov chains (discrete-time Markov processes on discrete state spaces) (60J10) Percolation (82B43) Branching processes (Galton-Watson, birth-and-death, etc.) (60J80)

Related Items (12)

Cluster capacity functionals and isomorphism theorems for Gaussian free fields ⋮ On coupling and ``Vacant set level set percolation ⋮ The sign clusters of the massless Gaussian free field percolate on \(\mathbb{Z}^{d}\), \(d \geqslant 3\) (and more) ⋮ Giant component for the supercritical level‐set percolation of the Gaussian free field on regular expander graphs ⋮ Isomorphism theorems, extended Markov processes and random interlacements ⋮ Anatomy of a Gaussian giant: supercritical level-sets of the free field on regular graphs ⋮ Percolation for the Gaussian free field on the cable system: counterexamples ⋮ Phase transition for level-set percolation of the membrane model in dimensions \(d \geq 5\) ⋮ Level-set percolation of the Gaussian free field on regular graphs II: finite expanders ⋮ Some percolations involving the Gaussian free fields ⋮ Level-set percolation of the Gaussian free field on regular graphs. I. Regular trees ⋮ Analyticity of Gaussian free field percolation observables

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