The critical density for the frog model is the degree of the tree

Abstract

The frog model on the rooted d-ary tree changes from transient to recurrent as the number of frogs per site is increased. We prove that the location of this transition is on the same order as the degree of the tree.

arXiv comment12 pages; final published version

References in corpus (4)

• A survey of max-type recursive distributional equations
• Phase transition for the frog model
• From transience to recurrence with Poisson tree frogs
• Recurrence for the frog model with drift on ${\mathbb{Z}}^d$

Cited by in corpus (8)

• Stochastic orders and the frog model
• Recurrence and Transience of Frogs with Drift on ${\mathbb{Z}}^d$
• Infection spread for the frog model on trees
• Frogs on trees?
• Cover time for the frog model on trees
• Sensitivity of the frog model to initial conditions
• Laws of large numbers for the frog model on the complete graph
• A stochastic combustion model with thresholds on trees