Consolidation rates for two interacting systems in the plane

Maury Bramson, J. Theodore Cox, David Griffeath

Research output: Contribution to journalArticlepeer-review

10 Scopus citations

Abstract

This paper is a sequel of a paper of Cox and Griffeath "diffusive clustering in the two dimensional voter model". We continue our study of the voter model and coalescing random walks on the two dimensional integer lattice. Some exact asymptotics concerning the rate of clustering in the former process and the coalescence rate of the latter are derived. We use these results to prove a limit law, announced in that earlier paper, concerning the size of the largest square centered at the origin which is of solid color at a large time t.

Original languageEnglish (US)
Pages (from-to)613-625
Number of pages13
JournalProbability Theory and Related Fields
Volume73
Issue number4
DOIs
StatePublished - Nov 1986

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