Fluctuations in the Aztec diamonds via a Lorentz-minimal surface

18 Feb 2020 Chelkak Dmitry Ramassamy Sanjay

We provide a new description of the scaling limit of dimer fluctuations in homogeneous Aztec diamonds via the intrinsic conformal structure of a Lorentz-minimal surface in $\mathbb{R}^{2+1}$. This surface naturally appears as the limit of the graphs of origami maps associated to symmetric t-embeddings (Coulomb gauges) of Aztec diamonds, fitting the framework of [CLR1,CLR2]...

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  • MATHEMATICAL PHYSICS
  • COMBINATORICS
  • MATHEMATICAL PHYSICS
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