A new upper bound for the critical probability of the frog model on homogeneous trees

Abstract

We consider the interacting particle system on the homogeneous tree of degree $(d+1)$, known as frog model. In this model, active particles perform independent random walks, awakening all sleeping particles they encounter, and dying after a random number of jumps, with geometric distribution. We prove an upper bound for the critical parameter of survival of the model, which improves the previously known results. This upper bound was conjectured in a paper by Lebensztayn et al. ($J.Stat.Phys.$, 119(1-2), 331-345, 2005). We also give a closed formula for the upper bound.

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• A new upper bound for the critical probability of the frog model on homogeneous trees
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Cited by in corpus (8)

• A new upper bound for the critical probability of the frog model on homogeneous trees
• On the existence of accessibility in a tree-indexed percolation model
• Laws of large numbers for the frog model on the complete graph
• Phase transition for the frog model on biregular trees
• CLT for the proportion of infected incividuals for an epidemic model on a complete graph
• Critical parameter of the frog model on homogeneous trees with geometric lifetime
• A stochastic combustion model with thresholds on trees
• A zero-one law for recurrence and transience of frog processes