Sensitivity of the frog model to initial conditions

DOI10.1214/19-ECP230zbMath1488.60235arXiv1809.03082MaRDI QIDQ2422724

Tobias Johnson, Leonardo T. Rolla

Publication date: 20 June 2019

Published in: Electronic Communications in Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1809.03082

zbMATH Keywords

recurrencefrog modeltransiencebranching random walkactivated random walk

Mathematics Subject Classification ID

Interacting random processes; statistical mechanics type models; percolation theory (60K35) Markov chains (discrete-time Markov processes on discrete state spaces) (60J10) Branching processes (Galton-Watson, birth-and-death, etc.) (60J80)

Related Items (6)

Transience and recurrence of sets for branching random walk via non-standard stochastic orders ⋮ Non-universality in clustered ballistic annihilation ⋮ Parking on supercritical Galton-Watson trees ⋮ Activated Random Walks on \(\mathbb{Z}^d\) ⋮ On transience of frogs on Galton-Watson trees ⋮ Diffusion-limited annihilating systems and the increasing convex order

Cites Work

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• From transience to recurrence with Poisson tree frogs
• Absorbing-state phase transition for driven-dissipative stochastic dynamics on \(\mathbb Z\)
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• The critical density for the frog model is the degree of the tree
• Stochastic orders and the frog model
• Critical density of activated random walks on transitive graphs
• Recurrence and transience for the frog model on trees
• Lindley-type equations in the branching random walk
• Non-fixation for conservative stochastic dynamics on the line
• Universality and sharpness in activated random walks
• Martingale convergence in the branching random walk

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