Site recurrence for coalescing random walk

Itai Benjamini; Eric Foxall; Ori Gurel-Gurevich; Matthew Junge; Harry Kesten

doi:10.1214/16-ECP5

Site recurrence for coalescing random walk

Itai Benjamini
, Eric Foxall
, Ori Gurel-Gurevich
, Matthew Junge
, Harry Kesten

Weizmann Institute of Science, The Hebrew University of Jerusalem

Research output: Contribution to journal › Article › peer-review

Abstract

Begin continuous time random walks from every vertex of a graph and have particles coalesce when they collide. We use a duality relation with the voter model to prove the process is site recurrent on bounded degree graphs, and for Galton-Watson trees whose offspring distribution has exponential tail. We prove bounds on the occupation probability of a site, as well as a general 0-1 law. Similar conclusions hold for a coalescing process on trees where particles do not backtrack.

Original language	English
Article number	47
Number of pages	12
Journal	Electronic Communications in Probability
Volume	21
DOIs	https://doi.org/10.1214/16-ECP5
State	Published - 2016

Keywords

Interacting particle system
Multiple random walks
Random walk
Recurrence

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty

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10.1214/16-ECP5

Cite this

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title = "Site recurrence for coalescing random walk",

abstract = "Begin continuous time random walks from every vertex of a graph and have particles coalesce when they collide. We use a duality relation with the voter model to prove the process is site recurrent on bounded degree graphs, and for Galton-Watson trees whose offspring distribution has exponential tail. We prove bounds on the occupation probability of a site, as well as a general 0-1 law. Similar conclusions hold for a coalescing process on trees where particles do not backtrack.",

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AU - Benjamini, Itai

AU - Foxall, Eric

AU - Gurel-Gurevich, Ori

AU - Junge, Matthew

AU - Kesten, Harry

PY - 2016

Y1 - 2016

N2 - Begin continuous time random walks from every vertex of a graph and have particles coalesce when they collide. We use a duality relation with the voter model to prove the process is site recurrent on bounded degree graphs, and for Galton-Watson trees whose offspring distribution has exponential tail. We prove bounds on the occupation probability of a site, as well as a general 0-1 law. Similar conclusions hold for a coalescing process on trees where particles do not backtrack.

AB - Begin continuous time random walks from every vertex of a graph and have particles coalesce when they collide. We use a duality relation with the voter model to prove the process is site recurrent on bounded degree graphs, and for Galton-Watson trees whose offspring distribution has exponential tail. We prove bounds on the occupation probability of a site, as well as a general 0-1 law. Similar conclusions hold for a coalescing process on trees where particles do not backtrack.

KW - Interacting particle system

KW - Multiple random walks

KW - Random walk

KW - Recurrence

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VL - 21

JO - Electronic Communications in Probability

JF - Electronic Communications in Probability

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Site recurrence for coalescing random walk

Abstract

Keywords

ASJC Scopus subject areas

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