# The voter model chordal interface in two dimensions

Mark Holmes, Yevhen Mohylevskyy, Charles Newman

Research output: Contribution to journalArticle

### 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 language English (US) 937-957 21 Journal of Statistical Physics 159 4 https://doi.org/10.1007/s10955-015-1198-9 Published - 2015

### Fingerprint

Voter Model
Two Dimensions
coalescing
Geometric object
Triangular Lattice
Vote
Stationarity
Walk
boxes

### Keywords

• Coalescing random walks
• Interface
• Percolation
• Voter model

### ASJC Scopus subject areas

• Statistical and Nonlinear Physics
• Mathematical Physics

### Cite this

The voter model chordal interface in two dimensions. / Holmes, Mark; Mohylevskyy, Yevhen; Newman, Charles.

In: Journal of Statistical Physics, Vol. 159, No. 4, 2015, p. 937-957.

Research output: Contribution to journalArticle

Holmes, Mark ; Mohylevskyy, Yevhen ; Newman, Charles. / The voter model chordal interface in two dimensions. In: Journal of Statistical Physics. 2015 ; Vol. 159, No. 4. pp. 937-957.
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