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Limit shapes and the complex Burgers equation

Richard Kenyon Department of Mathematics, Brown University Andrei Okounkov Department of Mathematics, Princeton University

TBD mathscidoc:1701.331988

Acta Mathematica, 199, (2), 263-302, 2005.11
In this paper we study surfaces in$R$^{3}that arise as limit shapes in random surface models related to planar dimers. These limit shapes are$surface tension minimizers$, that is, they minimize a functional of the form ∫$σ$(∇$h$)$dx$$dy$among all Lipschitz functions$h$taking given values on the boundary of the domain. The surface tension$σ$has singularities and is not strictly convex, which leads to formation of$facets$and$edges$in the limit shapes.
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@inproceedings{richard2005limit,
  title={Limit shapes and the complex Burgers equation},
  author={Richard Kenyon, and Andrei Okounkov},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203351240560697},
  booktitle={Acta Mathematica},
  volume={199},
  number={2},
  pages={263-302},
  year={2005},
}
Richard Kenyon, and Andrei Okounkov. Limit shapes and the complex Burgers equation. 2005. Vol. 199. In Acta Mathematica. pp.263-302. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203351240560697.
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