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Dimers and embeddings

Marianna Russkik
Monday, October 25, 2021 - 2:30pm to 3:30pm
Smith 305

We introduce a concept of ‘t-embeddings’ of weighted bipartite planar graphs. 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. We also develop a relevant theory of discrete holomorphic functions on t-embeddings; this theory unifies Kenyon’s holomorphic functions on T-graphs and s-holomorphic functions coming from the Ising model. We provide a meta-theorem on convergence of the height fluctuations to the Gaussian Free Field.

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