A Stochastic Combustion Model with Thresholds on Trees

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 in...

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Bibliographic Details
Published inJournal of statistical physics Vol. 190; no. 5
Main Authors Junge, Matthew, McDonald, Zoe, Pulla, Jean, Reeves, Lily
Format Journal Article
LanguageEnglish
Published New York Springer US 10.05.2023
Springer
Subjects
Combustion
Mathematical and Computational Physics
Physical Chemistry
Physics
Physics and Astronomy
Quantum Physics
Statistical Physics and Dynamical Systems
Theoretical
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Summary: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 the total number of root visits undergoes a phase transition.
ISSN:1572-9613
0022-4715
1572-9613
DOI:10.1007/s10955-023-03102-w