The branching random walk and contact process on Galton-Watson and nonhomogeneous trees

DOI10.1214/aop/1015345762zbMath1013.60078OpenAlexW1507972011MaRDI QIDQ1872236

Alan M. Stacey, Robin Pemantle

Publication date: 6 May 2003

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

Full work available at URL: https://doi.org/10.1214/aop/1015345762

zbMATH Keywords

treephase transitioncontact processbranching random walk

Mathematics Subject Classification ID

Interacting random processes; statistical mechanics type models; percolation theory (60K35) Random walks, random surfaces, lattice animals, etc. in equilibrium statistical mechanics (82B41)

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Cites Work

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• Multiple transition points for the contact process on the binary tree
• The existence of an intermediate phase for the contact process on trees
• Density and uniqueness in percolation
• Branching random walks on trees
• The contact process on trees
• Additive set-valued Markov processes and graphical methods
• A new proof that for the contact process on homogeneous trees local survival implies complete convergence
• Limit set of a weakly supercritical contact process on a homogeneous tree
• The second lowest extremal invariant measure of the contact process
• The second lowest extremal invariant measure of the contact process. II
• Biased random walks on Galton-Watson trees
• Anisotropic branching random walks on homogeneous trees
• Infinitely many contact process transitions on a tree
• Branching random walks and contact processes on homogeneous trees
• The critical contact process dies out
• Phase transitions on nonamenable graphs
• The contact process on finite homogeneous trees