Lozenge Tilings and Hurwitz Numbers

  title={Lozenge Tilings and Hurwitz Numbers},
  author={Jonathan Novak},
  journal={Journal of Statistical Physics},
  • Jonathan Novak
  • Published 28 July 2014
  • Mathematics, Physics
  • Journal of Statistical Physics
We give a new proof of the fact that, near a turning point of the frozen boundary, the vertical tiles in a uniformly random lozenge tiling of a large sawtooth domain are distributed like the eigenvalues of a GUE random matrix. Our argument uses none of the standard tools of integrable probability. In their place, it uses a combinatorial interpretation of the Harish-Chandra/Itzykson-Zuber integral as a generating function for desymmetrized Hurwitz numbers. 

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