Existence of phase transition for percolation using the Gaussian free field

DOI10.1215/00127094-2020-0036zbMath1470.60275arXiv1806.07733OpenAlexW3097796011MaRDI QIDQ2657466

Franco Severo, Subhajit Goswami, Hugo Duminil-Copin, Ariel Yadin, Aran Raoufi

Publication date: 12 March 2021

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1806.07733

zbMATH Keywords

isoperimetric inequalitypercolationphase transition

Mathematics Subject Classification ID

Interacting random processes; statistical mechanics type models; percolation theory (60K35) Graphs and abstract algebra (groups, rings, fields, etc.) (05C25) Percolation (82B43) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20)

Related Items (16)

Equality of critical parameters for percolation of Gaussian free field level sets ⋮ Continuity of the Ising phase transition on nonamenable groups ⋮ Transience and anchored isoperimetric dimension of supercritical percolation clusters ⋮ Gap at 1 for the percolation threshold of Cayley graphs ⋮ 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 ⋮ Analyticity Results in Bernoulli Percolation ⋮ On clusters of Brownian loops in \(d\) dimensions ⋮ Supercritical percolation on nonamenable graphs: isoperimetry, analyticity, and exponential decay of the cluster size distribution ⋮ Power-law bounds for critical long-range percolation below the upper-critical dimension ⋮ Percolation on an infinitely generated group ⋮ Coexistence of competing first passage percolation on hyperbolic graphs ⋮ A time-invariant random graph with splitting events ⋮ On the radius of Gaussian free field excursion clusters ⋮ Analyticity of Gaussian free field percolation observables ⋮ Explicit universal minimal constants for polynomial growth of groups

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