Strict monotonicity of percolation thresholds under covering maps

DOI10.1214/19-AOP1355zbMath1469.60338arXiv1803.09686OpenAlexW2989581725MaRDI QIDQ2189466

Franco Severo, Sébastien Martineau

Publication date: 15 June 2020

Published in: The Annals of Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1803.09686

zbMATH Keywords

percolationcritical pointstrict monotonicitycovering mapsquasi-transitive graphsMargulis-Russo formula

Mathematics Subject Classification ID

Interacting random processes; statistical mechanics type models; percolation theory (60K35) Phase transitions (general) in equilibrium statistical mechanics (82B26) Percolation (82B43)

Related Items (3)

Gap at 1 for the percolation threshold of Cayley graphs ⋮ Locality of percolation for graphs with polynomial growth ⋮ Covering monotonicity of the limit shapes of first passage percolation on crystal lattices

Cites Work

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• Critical percolation on any quasi-transitive graph of exponential growth has no infinite clusters
• The set of connective constants of Cayley graphs contains a Cantor space
• Density and uniqueness in percolation
• Stability of infinite clusters in supercritical percolation
• Percolation beyond \(\mathbb{Z}^ d\), many questions and a few answers
• Indistinguishability of percolation clusters
• Strict Inequalities for Connective Constants of Transitive Graphs
• Quantitative Estimates and Rigorous Inequalities for Critical Points of a Graph and Its Subgraphs
• Percolation
• Finiteness Conditions for Soluble Groups

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