A stochastic combustion model with thresholds on trees

Abstract

Place one active particle at the root of a graph and a Poisson-distributed number of dormant particles at the other vertices. Active particles perform simple random walk. Once the number of visits to a site reaches a random threshold, any dormant particles there become active. For this process on infinite $d$-ary trees, we show that total root visits undergoes a phase transition.

Published version

References in corpus (1)

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