Lozenge tilings and Hurwitz numbers
Mathematical Physics
2015-10-28 v2 Combinatorics
math.MP
Probability
Abstract
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.
Keywords
Cite
@article{arxiv.1407.7578,
title = {Lozenge tilings and Hurwitz numbers},
author = {Jonathan Novak},
journal= {arXiv preprint arXiv:1407.7578},
year = {2015}
}
Comments
9 pages, 3 figures. Version 2 fixes errors, adds clarifications and new material; title changed