Infection spread for the frog model on trees

Abstract

The frog model is an infection process in which dormant particles begin moving and infecting others once they become infected. We show that on the rooted $d$-ary tree with particle density $\Omega (d^2)$, the set of visited sites contains a linearly expanding ball and the number of visits to the root grows linearly with high probability.

EJP version; results on cover time on finite trees can be found at arXiv:1802.03428

References in corpus (10)

• The spread of a rumor or infection in a moving population
• From transience to recurrence with Poisson tree frogs
• Size biased couplings and the spectral gap for random regular graphs
• Recurrence for the frog model with drift on ${\mathbb{Z}}^d$
• Stochastic orders and the frog model
• Recurrence and Transience of Frogs with Drift on ${\mathbb{Z}}^d$
• The critical density for the frog model is the degree of the tree
• Frogs on trees?
• Cover time for the frog model on trees
• The nonhomogeneous frog model on $\mathbb{Z}$

Cited by in corpus (5)

• A new upper bound for the critical probability of the frog model on homogeneous trees
• Cover time for the frog model on trees
• Laws of large numbers for the frog model on the complete graph
• Deviation bounds for the first passage time in the frog model
• A stochastic combustion model with thresholds on trees