Around planar dimer models: Schur processes and integrable statistical mechanics on isoradial graphs

Abstract : The dimer model is a probability measure on perfect matchings (or dimer configurations) on a graph. Dimer models on some subgraphs of the honeycomb and square lattices, which by duality, correspond to tilings with rhombi and dominos, are directly related to Schur processes, probability measures on sequences of interlacing partitions. Via bijections and other combinatorial correspondences, other integrable models of two-dimensional statistical mechanics can be mapped to planar dimer models: spanning trees, the Ising model… This manuscript presents an overview of the results obtained by the author and his coauthors on questions around planar dimer models, with a strong emphasis, on one hand, on the relation with Schur processes, and on the other hand, on these models from statistical mechanics related to dimers, defined on isoradial graphs, a particular class of embedded planar graphs with interesting properties.
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Cédric Boutillier. Around planar dimer models: Schur processes and integrable statistical mechanics on isoradial graphs. Mathematics [math]. UPMC - Université Paris 6 Pierre et Marie Curie, 2016. ⟨tel-01411592⟩

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