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arXiv · 2209.08107

A stochastic combustion model with thresholds on trees

Matthew Junge·Zoe McDonald·Jean Pulla·Lily Reeves
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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.

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Matthew Junge, Zoe McDonald, Jean Pulla, Lily Reeves. 2022-09-16. A stochastic combustion model with thresholds on trees. https://doi.org/10.1007/s10955-023-03102-w

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