Non-Colliding Paths in the Honeycomb Dimer Model and the Dyson Process |
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Authors: | Cédric Boutillier |
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Affiliation: | (1) Laboratoire de Probabilités et Modèles Aléatoires, Université Pierre et Marie Curie, Paris VI, Case courrier 188, 4 Place Jussieu, 75252 Paris Cedex 05, France |
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Abstract: | In this paper we describe a natural family of random non-intersecting discrete paths in the dimer model on the honeycomb lattice. We show that when the dimer model is going to freeze, this family of paths, after a proper rescaling, converges to the extended sine process, obtained traditionally as the limit of the Dyson model when the number of particles goes to infinity. |
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Keywords: | Tilings Dimer models Phase transition Random matrices Dyson model |
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