Random dimer coverings of large planar graphs are known to exhibit unusual and visually apparent asymptotic phenomena that include formation of frozen regions and various phases in the unfrozen ones. For a specific family of subgraphs of the (periodically weighted) square lattice known as the Aztec diamonds, the asymptotic behavior of dimers admits a precise description in terms of geometry of underlying Riemann surfaces. The goal of the talk is to explain how the surface structure manifests itself through the statistics of dimers. Based on joint works with T. Berggren and M. Duits.
By Leonid Pastur
By Vadim Kaimanovich
By Tatiana Nagnibeda
By Mikhail Gromov
By Andrey Malyutin
By Anna Ershler
By Fyodor Petrov
By Alexander Chervov
By Vladimir Rubtsov
By Alexander Barvinok
By Hubert Lacoin
By Benoît Dagallier
