Relations between invasion percolation and critical percolation in two dimensions

DOI10.1214/09-AOP462zbMath1247.60134arXiv0806.2425OpenAlexW2107449886WikidataQ60843856 ScholiaQ60843856MaRDI QIDQ971942

Bálint Vágvölgyi, Michael Damron, Artëm Sapozhnikov

Publication date: 17 May 2010

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

Full work available at URL: https://arxiv.org/abs/0806.2425

zbMATH Keywords

correlation lengthinvasion percolationcritical percolationnear-critical percolationscaling relationsincipient infinite clusterinvasion ponds

Mathematics Subject Classification ID

Interacting random processes; statistical mechanics type models; percolation theory (60K35) Percolation (82B43)

Related Items (17)

The scaling limits of the minimal spanning tree and invasion percolation in the plane ⋮ Two-dimensional volume-frozen percolation: deconcentration and prevalence of mesoscopic clusters ⋮ Invasion percolation on Galton-Watson trees ⋮ Frozen percolation in two dimensions ⋮ Some toy models of self-organized criticality in percolation ⋮ Transitions for exceptional times in dynamical first-passage percolation ⋮ Limit theorems for 2D invasion percolation ⋮ Invasion percolation on the Poisson-weighted infinite tree ⋮ Exponential growth of ponds in invasion percolation on regular trees ⋮ Subdiffusivity of random walk on the 2D invasion percolation cluster ⋮ Superlinearity of Geodesic Length in 2D Critical First-Passage Percolation ⋮ Non-optimality of invaded geodesics in 2d critical first-passage percolation ⋮ Arm events in two-dimensional invasion percolation ⋮ Outlets of 2D invasion percolation and multiple-armed incipient infinite clusters ⋮ Local time on the exceptional set of dynamical percolation and the incipient infinite cluster ⋮ Harry Kesten's work in probability theory ⋮ Near-critical 2D percolation with heavy-tailed impurities, forest fires and frozen percolation

Cites Work

• Random spatial growth with paralyzing obstacles
• Near-critical percolation in two dimensions
• The incipient infinite cluster in two-dimensional percolation
• The fractal volume of the two-dimensional invasion percolation cluster
• Invasion percolation and the incipient infinite cluster in 2D
• Scaling relations for 2D-percolation
• Infinite clusters in percolation models
• The size of a pond in 2D invasion percolation
• Invasion percolation on regular trees
• Lectures on two-dimensional critical percolation
• Capillary displacement and percolation in porous media
• Percolation
• An Extension of the Borel-Cantelli Lemma
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