Non-Colliding Paths in the Honeycomb Dimer Model and the Dyson Process

Cédric Boutillier (1)

1 LPSM (UMR_8001) - Laboratoire de Probabilités, Statistique et Modélisation

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, converge to the extended sine process, obtained traditionally as the limit of the Dyson model when the number of particles goes to infinity.

Domaines: Probabilités [math.PR]

Cédric Boutillier. Non-Colliding Paths in the Honeycomb Dimer Model and the Dyson Process. Journal of Statistical Physics, 2007, 129 (5-6), pp.1117-1135. ⟨10.1007/s10955-007-9431-9⟩. ⟨hal-03896822⟩