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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Boutillier, C. Non-Colliding Paths in the Honeycomb Dimer Model and the Dyson Process. J Stat Phys 129, 1117–1135 (2007). https://doi.org/10.1007/s10955-007-9431-9
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DOI: https://doi.org/10.1007/s10955-007-9431-9