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arXiv · 1409.0136

The voter model chordal interface in two dimensions

Mark Holmes·Yevhen Mohylevskyy·Charles M. Newman
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Abstract

Consider the voter model on a box of side length $L$ (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 $L\rightarrow \infty$. 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.

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Mark Holmes, Yevhen Mohylevskyy, Charles M. Newman. 2014-08-30. The voter model chordal interface in two dimensions. https://doi.org/10.1007/s10955-015-1198-9

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