The voter model chordal interface in two dimensions

Mark Holmes, Yevhen Mohylevskyy, Charles M. Newman

Research output: Contribution to journalArticlepeer-review

Abstract

Consider the voter model on a box of side length $$L$$L (in the triangular lattice) with boundary votes fixed forever as type 0 or type 1 on two different halves of the boundary. Motivated by analogous questions in percolation, we study several geometric objects at stationarity, as $$L\rightarrow \infty $$L→∞. One is the interface between the (large—i.e., boundary connected) 0-cluster and 1-cluster. Another is the set of large “coalescing classes” determined by the coalescing walk process dual to the voter model.

Original languageEnglish (US)
Pages (from-to)937-957
Number of pages21
JournalJournal of Statistical Physics
Volume159
Issue number4
DOIs
StatePublished - 2015

Keywords

  • Coalescing random walks
  • Interface
  • Percolation
  • Voter model

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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