Sharpness of the phase transition and exponential decay of the subcritical cluster size for percolation on quasi-transitive graphs

DOI10.1007/s10955-007-9459-xzbMath1214.82028arXiv0707.1089OpenAlexW3100945840WikidataQ59312010 ScholiaQ59312010MaRDI QIDQ2482266

Ivan Veselić, Tonci Antunovic

Publication date: 16 April 2008

Published in: Journal of Statistical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0707.1089

zbMATH Keywords

phase transitionrandom graphssite percolationquasi-transitive graphsedge percolation

Mathematics Subject Classification ID

Phase transitions (general) in equilibrium statistical mechanics (82B26) Percolation (82B43) Critical phenomena in equilibrium statistical mechanics (82B27)

Related Items (18)

A new proof of the sharpness of the phase transition for Bernoulli percolation and the Ising model ⋮ Percolation and isoperimetry on roughly transitive graphs ⋮ Critical percolation on any quasi-transitive graph of exponential growth has no infinite clusters ⋮ Homology-changing percolation transitions on finite graphs ⋮ Lifshitz asymptotics for percolation Hamiltonians ⋮ Percolation on infinite graphs and isoperimetric inequalities ⋮ A stochastic spatial model for the sterile insect control strategy ⋮ Analyticity Results in Bernoulli Percolation ⋮ Uniform approximation of the integrated density of states for long-range percolation Hamiltonians ⋮ An interlacing technique for spectra of random walks and its application to finite percolation clusters ⋮ Nonuniqueness and mean-field criticality for percolation on nonunimodular transitive graphs ⋮ Percolation on a product of two trees ⋮ A Banach space-valued ergodic theorem for amenable groups and applications ⋮ Percolation on hyperbolic graphs ⋮ Percolation Hamiltonians ⋮ Equality of Lifshitz and van Hove exponents on amenable Cayley graphs ⋮ Unions of random walk and percolation on infinite graphs ⋮ Sharpness for inhomogeneous percolation on quasi-transitive graphs

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