Lozenge Tilings, Glauber Dynamics and Macroscopic Shape

@article{Laslier2015LozengeTG,
  title={Lozenge Tilings, Glauber Dynamics and Macroscopic Shape},
  author={Benoit Laslier and Fabio Lucio Toninelli},
  journal={Communications in Mathematical Physics},
  year={2015},
  volume={338},
  pages={1287-1326}
}
We study the Glauber dynamics on the set of tilings of a finite domain of the plane with lozenges of side 1/L. Under the invariant measure of the process (the uniform measure over all tilings), it is well known (Cohn et al. J Am Math Soc 14:297–346, 2001) that the random height function associated to the tiling converges in probability, in the scaling limit $${L {\to} {\infty}}$$L→∞, to a non-trivial macroscopic shape minimizing a certain surface tension functional. According to the boundary… Expand

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