Corpus ID: 237503730

Bipartite dimer model: perfect t-embeddings and Lorentz-minimal surfaces

@inproceedings{Chelkak2021BipartiteDM,
  title={Bipartite dimer model: perfect t-embeddings and Lorentz-minimal surfaces},
  author={Dmitry Chelkak and Benoit Laslier and Marianna Russkikh},
  year={2021}
}
This is the second paper in the series devoted to the study of the dimer model on t-embeddings of planar bipartite graphs. We introduce the notion of perfect t-embeddings and assume that the graphs of the associated origami maps converge to a Lorentz-minimal surface Sξ as δ → 0. In this setup we prove (under very mild technical assumptions) that the gradients of the height correlation functions converge to those of the Gaussian Free Field defined in the intrinsic metric of the surface Sξ. We… Expand

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References

SHOWING 1-10 OF 32 REFERENCES
Dimer model and holomorphic functions on t-embeddings of planar graphs
We introduce the framework of discrete holomorphic functions on t-embeddings of weighted bipartite planar graphs; t-embeddings also appeared under the name Coulomb gauges in a recent workExpand
Dimers and imaginary geometry
We present a general result which shows that the winding of the branches in a uniform spanning tree on a planar graph converge in the limit of fine mesh size to a Gaussian free field. The resultExpand
Conformal invariance of dimer heights on isoradial double graphs
  • Zhongyang Li
  • Mathematics
  • 2013
An isoradial graph is a planar graph in which each face is inscribable into a circle of common radius. We study the 2-dimensional perfect matchings on a bipartite isoradial graph, obtained from theExpand
Dimers and circle patterns
We establish a correspondence between the dimer model on a bipartite graph and a circle pattern with the combinatorics of that graph, which holds for graphs that are either planar or embedded on theExpand
Dimers and amoebae
We study random surfaces which arise as height functions of random perfect matchings (a.k.a. dimer configurations) on a weighted, bipartite, doubly periodic graph G embedded in the plane. We deriveExpand
Conformal invariance of domino tiling
Let U be a multiply connected region in R 2 with smooth boundary. Let P∈be a polyomino in ∈Z 2 approximating U as ∈ → 0. We show that, for certain boundary conditions on P∈, the height distributionExpand
Dimers in Piecewise Temperleyan Domains
We study the large-scale behavior of the height function in the dimer model on the square lattice. Richard Kenyon has shown that the fluctuations of the height function on Temperleyan discretizationsExpand
Height Fluctuations in the Honeycomb Dimer Model
We study a model of random surfaces arising in the dimer model on the honeycomb lattice. For a fixed “wire frame” boundary condition, as the lattice spacing ϵ → 0, Cohn, Kenyon and Propp [3] showedExpand
Dominos in hedgehog domains
We introduce a new class of discrete approximations of planar domains that we call "hedgehog domains". In particular, this class of approximations contains two-step Aztec diamonds and similar shapes.Expand
Dimers, tilings and trees
TLDR
A natural equivalence is described between three planar objects: weighted bipartite planar graphs; planar Markov chains; and tilings with convex polygons, and the resulting "almost periodic" tilings and harmonic functions are classified. Expand
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