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.

arXiv commentPublished version

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