On the uniqueness of the infinite cluster in the percolation model

DOI10.1007/BF01229454zbMath0649.60104OpenAlexW2040264077MaRDI QIDQ1105927

Lucio Russo, Alberto Gandolfi, Geoffrey R. Grimmett

Publication date: 1988

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01229454

zbMATH Keywords

percolation modeluniqueness of the infinite open cluster

Mathematics Subject Classification ID

Interacting random processes; statistical mechanics type models; percolation theory (60K35)

Related Items

Density and uniqueness in percolation, A lower bound on the two-arms exponent for critical percolation on the lattice, Lucio Russo: probability theory and current interests, Uniqueness in percolation theory, On the four-arm exponent for 2D percolation at criticality, Uniqueness of the infinite component in a random graph with applications to percolation and spin glasses, Random cluster models on the triangular lattice, An upper bound on the two-arms exponent for critical percolation on \(\mathbb{Z}^d\), Locality of the critical probability for transitive graphs of exponential growth, Percolation in half-spaces: Equality of critical densities and continuity of the percolation probability

Cites Work

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• Uniqueness of the infinite cluster and continuity of connectivity functions for short and long range percolation
• On the uniqueness of the infinite occupied cluster in dependent two- dimensional site percolation
• Infinite clusters in percolation models
• On the Differentiability of the Number of Clusters Per Vertex in the Percolation Model