LA Probability Forum

UCLA, in Math Sciences Room 6627

The dimer model is a model from statistical mechanics corresponding to random perfect matchings on graphs. Circle patterns are a class of embeddings of planar graphs such that every face admits a circumcircle. We introduce a concept of ‘t-embeddings' (or a circle pattern) of a dimer planar graph, and discuss algebro-geometric properties of these embeddings. We believe that these t-embeddings always exist and that they are good candidates to recover the complex structure of big bipartite planar graphs carrying a dimer model.