The critical probability for the frog model is not a monotonic function of the graph

DOI10.1239/jap/1077134688zbMath1051.60095OpenAlexW2012968842MaRDI QIDQ4819458

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Publication date: 24 September 2004

Published in: Journal of Applied Probability (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1239/jap/1077134688

zbMATH Keywords

graphpercolationphase transitioncritical probabilityfrog model

Mathematics Subject Classification ID

Network design and communication in computer systems (68M10) Interacting random processes; statistical mechanics type models; percolation theory (60K35) Markov chains (discrete-time Markov processes on discrete state spaces) (60J10) Percolation (82B43)

Related Items (13)

Brownian snails with removal: epidemics in diffusing populations ⋮ Frog models on trees through renewal theory ⋮ Stochastic orders and the frog model ⋮ Infinite rate symbiotic branching on the real line: the tired frogs model ⋮ The frog model on trees with drift ⋮ On a one-dimensional model of infection spreading ⋮ Recurrence and transience of frogs with drift on \(\mathbb{Z}^d\) ⋮ Local and Global Survival for Nonhomogeneous Random Walk Systems on Z ⋮ An improved upper bound for the critical probability of the frog model on homogeneous trees ⋮ Laws of large numbers for the frog model on the complete graph ⋮ A new upper bound for the critical probability of the frog model on homogeneous trees ⋮ On the minimal drift for recurrence in the frog model on \(d\)-ary trees ⋮ Critical parameter of the frog model on homogeneous trees with geometric lifetime

Cites Work

• Unnamed Item
• Percolation beyond \(\mathbb{Z}^ d\), many questions and a few answers
• Phase transition for the frog model

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