LA Probability Forum

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.