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

References in corpus (9)

• Local statistics for random domino tilings of the Aztec diamond
• Random Domino Tilings and the Arctic Circle Theorem
• Inhomogeneous field theory inside the arctic circle
• Fluctuations of particle systems determined by Schur generating functions
• Asymptotic domino statistics in the Aztec diamond
• Dimers and Circle patterns
• Inhomogeneous Gaussian Free Field inside the interacting arctic curve
• Bipartite dimer model: perfect t-embeddings and Lorentz-minimal surfaces
• Perfect t-embeddings of uniformly weighted Aztec diamonds and tower graphs

Cited by in corpus (1)

• Möbius invariant Y-systems (cluster structures) for Miquel dynamics