corteel

Sylvie Corteel

"Dimers on Rail Yard Graphs"

We introduce a general model of dimer coverings of certain plane bipartite graphs, which we call Rail Yard Graphs (RYG). Using a transfer matrix approach and the celebrated boson-fermion correspondence, the model can be reformulated as a Schur process (i.e. a random sequence of integer partitions). We obtain explicit expressions for the partition function and for the inverse Kasteleyn matrix, which yields all dimer correlation functions. Plane partitions, domino tilings of the Aztec diamond and pyramid partitions arise as particular cases of our model.

This is joint work with Cédric Boutillier (Paris 6), Jérémie Bouttier (CEA), Guillaume Chapuy (CNRS) and Sanjay Ramassamy (Brown U.).