Lozenge Tilings and Hurwitz Numbers

被引:0
作者
Jonathan Novak
机构
[1] Massachusetts Institute of Technology,Department of Mathematics
来源
Journal of Statistical Physics | 2015年 / 161卷
关键词
Random tilings; Random matrices; Hurwitz numbers;
D O I
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中图分类号
学科分类号
摘要
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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页码:509 / 517
页数:8
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