The bead model and limit behaviors of dimer models
Abstract
In this paper, we study the bead model: beads are threaded on a set of wires on the plane represented by parallel straight lines. We add the constraint that between two consecutive beads on a wire; there must be exactly one bead on each neighboring wire. We construct a one-parameter family of Gibbs measures on the bead configurations that are uniform in a certain sense. When endowed with one of these measures, this model is shown to be a determinantal point process, whose marginal on each wire is the sine process (given by eigenvalues of large hermitian random matrices). We prove then that this process appears as a limit of any dimer model on a planar bipartite graph when some weights degenerate.
Keywords
Cite
@article{arxiv.math/0607162,
title = {The bead model and limit behaviors of dimer models},
author = {Cédric Boutillier},
journal= {arXiv preprint arXiv:math/0607162},
year = {2011}
}
Comments
Published in at http://dx.doi.org/10.1214/08-AOP398 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)