Fluctuations in the Aztec diamonds via a space-like maximal surface in Minkowski 3-space

Abstract

We provide a new description of the scaling limit of dimer fluctuations in homogeneous Aztec diamonds via the intrinsic conformal structure of a space-like maximal surface in the three-dimensional Minkowski space ${\mathbb{R}}^{2,1}$. This surface naturally appears as the limit of the graphs of origami maps associated to symmetric t-embeddings of Aztec diamonds, fitting the framework recently developed in arXiv:2109.06272.

13 pages, 6 figures. Final version accepted for publication in Confluentes Mathematici