Simultaneous uniqueness of infinite clusters in stationary random labeled graphs

DOI10.1007/BF02099583zbMath0827.60080MaRDI QIDQ1842613

Kenneth S. Alexander

Publication date: 26 November 1995

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

zbMATH Keywords

uniquenesslattice modelsrandom graphinvasion percolationcontinuum percolation

Mathematics Subject Classification ID

Random graphs (graph-theoretic aspects) (05C80) Interacting random processes; statistical mechanics type models; percolation theory (60K35) Percolation (82B43)

Related Items (6)

Weak laws of large numbers in geometric probability ⋮ The central limit theorem for Euclidean minimal spanning trees. I ⋮ Rate of convergence of power-weighted Euclidean minimal spanning trees ⋮ Boundedness of level lines for two-dimensional random fields ⋮ Near-minimal spanning trees: A scaling exponent in probability models ⋮ Dynamic Boolean models

Cites Work

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• Density and uniqueness in percolation
• Asymptotics for Euclidean minimal spanning trees on random points
• Uniqueness of the infinite component in a random graph with applications to percolation and spin glasses
• Uniqueness of unbounded occupied and vacant components in Boolean models
• Discontinuity of the percolation density in one dimensional \(1/| x- y| ^ 2\) percolation models
• Infinite clusters in percolation models
• On a continuum percolation model
• The supercritical phase of percolation is well behaved
• Long range percolation in stationary point processes

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