Fluctuations in the Aztec diamonds via a Lorentz-minimal surface
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 surface in the three-dimensional Minkowski space $\mathbb{R}^{2,1}$ with vanishing mean curvature. 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.
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Mathematical Physics
Combinatorics
Mathematical Physics
Probability