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January 2009 The bead model and limit behaviors of dimer models
Cédric Boutillier
Ann. Probab. 37(1): 107-142 (January 2009). DOI: 10.1214/08-AOP398

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.

Citation

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Cédric Boutillier. "The bead model and limit behaviors of dimer models." Ann. Probab. 37 (1) 107 - 142, January 2009. https://doi.org/10.1214/08-AOP398

Information

Published: January 2009
First available in Project Euclid: 17 February 2009

zbMATH: 1171.82006
MathSciNet: MR2489161
Digital Object Identifier: 10.1214/08-AOP398

Subjects:
Primary: 82B20

Rights: Copyright © 2009 Institute of Mathematical Statistics

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Vol.37 • No. 1 • January 2009
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