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A Stochastic Combustion Model with Thresholds on Trees

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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 the total number of root visits undergoes a phase transition.

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Authors and Affiliations

  1. Baruch College, New York, USA

    Matthew Junge & Jean Pulla

  2. Boston University, Boston, USA

    Zoe McDonald

  3. Cornell University, Ithaca, USA

    Lily Reeves

Authors
  1. Matthew Junge
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  2. Zoe McDonald
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  3. Jean Pulla
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  4. Lily Reeves
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Corresponding author

Correspondence to Matthew Junge.

Additional information

Communicated by Pablo A Ferrari.

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The authors received partial support from NSF grant DMS-1855516. Part of this research was completed during the 2021 Baruch College Discrete Math REU partially supported by NSF grant DMS-2051026. We are grateful to Tobias Johnson for his valuable input.

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Junge, M., McDonald, Z., Pulla, J. et al. A Stochastic Combustion Model with Thresholds on Trees. J Stat Phys 190, 100 (2023). https://doi.org/10.1007/s10955-023-03102-w

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  • DOI: https://doi.org/10.1007/s10955-023-03102-w

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