Lozenge Tilings and Hurwitz Numbers
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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.
Date issued
2015-07Department
Massachusetts Institute of Technology. Department of MathematicsJournal
Journal of Statistical Physics
Publisher
Springer US
Citation
Novak, Jonathan. “Lozenge Tilings and Hurwitz Numbers.” Journal of Statistical Physics 161.2 (2015): 509–517.
Version: Author's final manuscript
ISSN
0022-4715
1572-9613