Invasion percolation on regular trees

DOI10.1214/07-AOP346zbMath1145.60050arXivmath/0608132MaRDI QIDQ2482278

Gordon Slade, Omer Angel, Jesse Goodman, W. Th. F. den Hollander

Publication date: 16 April 2008

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

Full work available at URL: https://arxiv.org/abs/math/0608132

zbMATH Keywords

simple random walkPoisson point processcluster sizeincipient infinite clusterinvasion percolation clusterr-point function

Mathematics Subject Classification ID

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

Related Items (max. 100)

The scaling limits of the minimal spanning tree and invasion percolation in the plane ⋮ Invasion percolation on Galton-Watson trees ⋮ Randomly trapped random walks ⋮ Scaling limit of the invasion percolation cluster on a regular tree ⋮ Multisource invasion percolation on the complete graph ⋮ Limit theorems for 2D invasion percolation ⋮ Long paths in first passage percolation on the complete graph. I: Local PWIT dynamics ⋮ 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 ⋮ Random walk on the incipient infinite cluster for oriented percolation in high dimensions ⋮ Relations between invasion percolation and critical percolation in two dimensions ⋮ A random walk on \(\mathbb Z\) with drift driven by its occupation time at zero ⋮ Local time on the exceptional set of dynamical percolation and the incipient infinite cluster

Cites Work

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• Infinite canonical super-Brownian motion and scaling limits
• Mean-field critical behaviour for percolation in high dimensions
• Random walk on the incipient infinite cluster for oriented percolation in high dimensions
• The incipient infinite cluster in two-dimensional percolation
• Subdiffusive behavior of random walk on a random cluster
• Triangle condition for oriented percolation in high dimensions
• Invasion percolation and the incipient infinite cluster in 2D
• Construction of the Incipient Infinite cluster for spread-out oriented percolation above \(4 + 1\) dimensions
• Convergence of critical oriented percolation to super-Brownian motion above \(4+1\) dimensions
• Random walk on the incipient infinite cluster on trees

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