Journal article
The voter model chordal interface in two dimensions
M Holmes, Y Mohylevskyy, CM Newman
Journal of Statistical Physics | SPRINGER | Published : 2015
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.
Grants
Awarded by National Science Foundation
Funding Acknowledgements
We thank two referees for their suggestions, which led to significant improvements in the paper. MH thanks David Wilson for helpful discussions at the initial stages of this Project. MH and YM thank Raghu Varadhan, Federico Camia, and Pierre Nolin for helpful discussions and the Centre for eResearch at U. Auckland for providing the computing resources and support. The work of MH and YM was supported by an FRDF Grant from U. Auckland. The work of CMN was supported in part by US NSF Grants OISE-0730136 and DMS-1007524.