Frogs and some other interacting random walks models

Serguei Yu. Popov

doi:10.46298/dmtcs.3328

Serguei Yu. Popov - Frogs and some other interacting random walks models

dmtcs:3328 - Discrete Mathematics & Theoretical Computer Science, January 1, 2003, DMTCS Proceedings vol. AC, Discrete Random Walks (DRW'03) - https://doi.org/10.46298/dmtcs.3328

Frogs and some other interacting random walks modelsConference paper

Authors: Serguei Yu. Popov ¹

1 Instituto de Matemática e Estatística

We review some recent results for a system of simple random walks on graphs, known as \emphfrog model. Also, we discuss several modifications of this model, and present a few open problems. A simple version of the frog model can be described as follows: There are active and sleeping particles living on some graph. Each active particle performs a simple random walk with discrete time and at each moment it may disappear with probability 1-p. When an active particle hits a sleeping particle, the latter becomes active.

https://doi.org/10.46298/dmtcs.3328

Source: HAL:hal-01183923v1

Volume: DMTCS Proceedings vol. AC, Discrete Random Walks (DRW'03)

Section: Proceedings

Published on: January 1, 2003

Imported on: May 10, 2017

Keywords: [INFO.INFO-DS]Computer Science [cs]/Data Structures and Algorithms [cs.DS], [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM], [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO], [INFO.INFO-CG]Computer Science [cs]/Computational Geometry [cs.CG], [en] simple random walk, critical probability, shape theorem, recurrence

Bibliographic References

11 Documents citing this article

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Itai Benjamini;Luiz Renato Fontes;Jonathan Hermon;Fábio Prates Machado, 2020, On an epidemic model on finite graphs, The Annals of Applied Probability, 30, 1, 10.1214/19-aap1500, https://doi.org/10.1214/19-aap1500.

Matthew Junge, 2020, Critical Percolation and A+B$$\rightarrow $$2A Dynamics, arXiv (Cornell University), 181, 2, pp. 738-751, 10.1007/s10955-020-02597-x, http://arxiv.org/abs/1906.00988.

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Christopher Hoffman;Tobias Johnson;Matthew Junge, 2017, Recurrence and transience for the frog model on trees, arXiv (Cornell University), 45, 5, 10.1214/16-aop1125, http://arxiv.org/abs/1404.6238.

Christopher Hoffman;Tobias Johnson;Matthew Junge, 2016, From transience to recurrence with Poisson tree frogs, arXiv (Cornell University), 26, 3, 10.1214/15-aap1127, http://arxiv.org/abs/1501.05874.

Elena Kosygina;Martin P. W. Zerner, 2016, A zero-one law for recurrence and transience of frog processes, Probability Theory and Related Fields, 168, 1-2, pp. 317-346, 10.1007/s00440-016-0711-7.

Christian Döbler;Lorenz Pfeifroth, 2014, Recurrence for the frog model with drift on $\mathbb{Z}^d$, Electronic Communications in Probability, 19, none, 10.1214/ecp.v19-3740, https://doi.org/10.1214/ecp.v19-3740.

Irina Kurkova;Serguei Popov;M. Vachkovskaia, 2004, On Infection Spreading and Competition between Independent Random Walks, Electronic Journal of Probability, 9, none, 10.1214/ejp.v9-197, https://doi.org/10.1214/ejp.v9-197.

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