Cédric Boutillier
Published 2006-07-06, updated 2011-02-23Version 2
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.
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)
Journal: Annals of Probability 2009, Vol. 37, No. 1, 107-142
Universality of fluctutations in the dimer model
The dimer model on Riemann surfaces, I
Uniformly positive correlations in the dimer model and phase transition in lattice permutations on $\mathbb{Z}^d$, $d > 2$, via reflection positivity
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