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LA Probability Forum

Thursday, February 29, 2024
4:00pm to 5:00pm
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Perfect t-embedding of uniformly weighted Aztec diamond
Marianna Russkikh, Department of Mathematics, University of Notre Dame,

UCLA, Math Sciences Room 6627

A new type of graph embedding called a t-embedding, was recently introduced and used to prove the convergence of dimer model height fluctuations to a Gaussian Free Field (GFF) in a naturally associated metric, under certain technical assumptions. We study the properties of t-embeddings of uniform Aztec diamond graphs, and in particular utilize the integrability of the "shuffling algorithm" on these graphs to provide a precise asymptotic analysis of t-embeddings and verify the validity of the technical assumptions required for convergence. As a consequence, we complete a new proof of GFF fluctuations for the dimer model height function on the uniformly weighted Aztec diamond.

For more information, please contact Math Dept by phone at 626-395-4335 or by email at [email protected].