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Site recurrence for coalescing random walk
Itaï Benjaminia b, Eric Foxallc d, Ori Gurel-Gureviche f, Matthew Jungeg h, Harry Kesteni j
- aDepartment of Mathematics , Weizmann Institute
- bDepartment of Mathematics, Weizmann Institute
- cDepartment of Mathematical and Statistical Sciences , Arizona State University
- dDepartment of Mathematical and Statistical Sciences, Arizona State University
- eEinstein Institute of Mathematics , Hebrew University of Isreal
- fEinstein Institute of Mathematics, Hebrew University of Isreal
- gUniversity of Washington , United States of America
- hUniversity of Washington, United States of America
- iDepartment of Mathematics , Cornell University
- jDepartment of Mathematics, Cornell University
Electronic Communications in ProbabilityInstitute of Mathematical Statistics2016-01-01 8 citations13 references
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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.