Formation of an interface by competitive erosion
Probability
2015-01-16 v1 Statistical Mechanics
Abstract
In 2006, the fourth author proposed a graph-theoretic model of interface dynamics called competitive erosion. Each vertex of the graph is occupied by a particle that can be either red or blue. New red and blue particles alternately get emitted from their respective bases and perform random walk. On encountering a particle of the opposite color they kill it and occupy its position. We prove that on the cylinder graph (the product of a path and a cycle) an interface spontaneously forms between red and blue and is maintained in a predictable position with high probability.
Cite
@article{arxiv.1501.03584,
title = {Formation of an interface by competitive erosion},
author = {Shirshendu Ganguly and Lionel Levine and Yuval Peres and James Propp},
journal= {arXiv preprint arXiv:1501.03584},
year = {2015}
}
Comments
47 pages, 11 figures