Matthew Nicoletti - Perfect t-embeddings of uniform Aztec diamond graphs - IPAM at UCLA

March 29, 2024
Recorded 29 March 2024. Matthew Nicoletti of the Massachusetts Institute of Technology presents "Perfect t-embeddings of uniform Aztec diamond graphs" at IPAM's Statistical Mechanics and Discrete Geometry Workshop. Abstract: Chelkak, Laslier, and Russkikh introduce a new type of graph embedding called a t-embedding, and use it to prove the convergence of dimer model height fluctuations to a Gaussian Free Field (GFF) in a naturally associated metric, under certain technical assumptions. Building on a work of Chelkak and Ramassamy, we study the properties of "perfect" t-embeddings of uniform Aztec diamond graphs, and in particular utilize the integrability of the “shuffling algorithm” on these graphs to give new exact formulas for the t-embeddings. We use these to provide a precise asymptotic analysis of the t-embeddings, in order to verify the validity of the technical assumptions required for convergence to the GFF. As a consequence, we complete a new proof of GFF fluctuations for the dimer model height function on the uniformly weighted Aztec diamond. Learn more online at: