The Annals of Probability
- Ann. Probab.
- Volume 37, Number 1 (2009), 107-142.
The bead model and limit behaviors of dimer models
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.
Ann. Probab., Volume 37, Number 1 (2009), 107-142.
First available in Project Euclid: 17 February 2009
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 82B20: Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs
Boutillier, Cédric. The bead model and limit behaviors of dimer models. Ann. Probab. 37 (2009), no. 1, 107--142. doi:10.1214/08-AOP398. https://projecteuclid.org/euclid.aop/1234881686