Skip to main contentSkip to search
Episciences
Open Access Journals
Sign in(new window)
Discrete Mathematics & Theoretical Computer Science logo
Discrete Mathematics & Theoretical Computer Science
Discrete Mathematics & Theoretical Computer Science logo
Discrete Mathematics & Theoretical Computer Science
Sign in(new window)
Articles & Issues
All articlesAll accepted articlesAll volumesLast volumeSectionsSpecial issuesAuthors
About
The journalIndexing
Boards
Publish
For authorsEthical charter
Submit
Discrete Mathematics & Theoretical Computer Science logo
Contact
|
Credits
eISSN 1365-8050
|
RSS
|
Atom
Episciences
Documentation
|
Acknowledgements
|
Publishing policy
Accessibility: non-compliant
|
Legal mentions
|
Privacy statement
|
Terms of use
  1. Home > Articles & Issues >
  2. Articles >
  3. Frogs and some other ...
Conference paper

Frogs and some other interacting random walks models

Serguei Yu. Popov (1) (2)
(1) Instituto de Matemática e Estatística
(2) Instituto de Matemática, Estatística e Ciência da Computação [Universidade de São Paulo]
Download article
Open on HAL
Imported on
May 10, 2017
Published on
December 31, 2002
Last modified on
March 31, 2025
Volume 0
DMTCS Proceedings vol. AC, Discrete Random Walks (DRW'03)
Proceedings
DOI
10.46298/dmtcs.3328
License
https://about.hal.science/hal-authorisation-v1
Indicators
1565
Views
2180
Downloads

Frogs and some other interacting random walks models

Serguei Yu. Popov (1) (2)
(1) Instituto de Matemática e Estatística
(2) Instituto de Matemática, Estatística e Ciência da Computação [Universidade de São Paulo]
Abstract
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.
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]
  • simple random walk
  • critical probability
  • shape theorem
  • recurrence
Cited by

Source: OpenCitations

  • On an epidemic model on finite graphs

    The Annals of Applied Probability

    Authors : Itai Benjamini, Luiz Renato Fontes ORCID, Jonathan Hermon ORCID, Fábio Prates Machado ORCID

    Journal reference : Volume 30, 2020, pp.

    DOI : 10.1214/19-aap1500
  • A Stochastic Combustion Model with Thresholds on Trees

    Journal of Statistical Physics

    Authors : Matthew Junge ORCID, Zoe McDonald, Jean Pulla, Lily Reeves ORCID

    Journal reference : Volume 190, 2023, pp.

    DOI : 10.1007/s10955-023-03102-w
  • Critical Percolation and A+B$$\rightarrow $$2A Dynamics

    arXiv (Cornell University)

    Authors : Matthew Junge ORCID

    Journal reference : Volume 181, 2020, pp. 738-751

    DOI : 10.1007/s10955-020-02597-x
  • A zero-one law for recurrence and transience of frog processes

    Probability Theory and Related Fields

    Authors : Elena Kosygina ORCID, Martin P. W. Zerner

    Journal reference : Volume 168, 2016, pp. 317-346

    DOI : 10.1007/s00440-016-0711-7
  • Improved critical drift estimates for the frog model on trees

    Electronic Communications in Probability

    Authors : Poly Mathews Jr.

    Journal reference : Volume 29, 2024, pp.

    DOI : 10.1214/24-ecp606
  • From transience to recurrence with Poisson tree frogs

    arXiv (Cornell University)

    Authors : Christopher Hoffman, Tobias Johnson ORCID, Matthew Junge ORCID

    Journal reference : Volume 26, 2016, pp.

    DOI : 10.1214/15-aap1127
  • A Continuous-Time Urn Model for a System of Activated Particles

    Mathematics

    Authors : Rafik Aguech ORCID, Hanene Mohamed

    Journal reference : Volume 11, 2023, pp. 4967

    DOI : 10.3390/math11244967
  • Brownian snails with removal die out in one dimension

    Electronic Communications in Probability

    Authors : Ivailo Hartarsky ORCID, Lyuben Lichev ORCID

    Journal reference : Volume 28, 2023, pp.

    DOI : 10.1214/23-ecp551
  • Brownian snails with removal: epidemics in diffusing populations

    Electronic Journal of Probability

    Authors : Geoffrey R. Grimmett ORCID, Zhongyang Li ORCID

    Journal reference : Volume 27, 2022, pp.

    DOI : 10.1214/22-ejp804
  • On Infection Spreading and Competition between Independent Random Walks

    Electronic Journal of Probability

    Authors : Irina Kurkova, Serguei Popov ORCID, M. Vachkovskaia ORCID

    Journal reference : Volume 9, 2004, pp.

    DOI : 10.1214/ejp.v9-197
  • Spread of an infection on the zero range process

    Annales de l Institut Henri Poincaré Probabilités et Statistiques

    Authors : Rangel Baldasso, Augusto Teixeira

    Journal reference : Volume 56, 2020, pp.

    DOI : 10.1214/19-aihp1021
  • Infinite rate symbiotic branching on the real line: The tired frogs model

    Annales de l Institut Henri Poincaré Probabilités et Statistiques

    Authors : Achim Klenke, Leonid Mytnik ORCID

    Journal reference : Volume 56, 2020, pp.

    DOI : 10.1214/19-aihp986
  • Recurrence and transience for the frog model on trees

    The Annals of Probability

    Authors : Christopher Hoffman, Tobias Johnson, Matthew Junge

    Journal reference : Volume 45, 2017, pp.

    DOI : 10.1214/16-aop1125
  • Recurrence for the frog model with drift on $\mathbb{Z}^d$

    Electronic Communications in Probability

    Authors : Christian Döbler ORCID, Lorenz Pfeifroth

    Journal reference : Volume 19, 2014, pp.

    DOI : 10.1214/ecp.v19-3740
  • Recurrence and transience of contractive autoregressive processes and related Markov chains

    Electronic Journal of Probability

    Authors : Martin P.W. Zerner

    Journal reference : Volume 23, 2018, pp.

    DOI : 10.1214/18-ejp152
Preview
Loading PDF preview...