Lozenge Tilings and Hurwitz Numbers
Name
10955_2015_Article_1330.pdf
Size
509.44 KB
Format
Adobe PDF
Checksum (MD5)
4392a754c2226bd73358bc737de09f8f
Author(s)
Novak, Jonathan
Date Issued
July 2015
Journal
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
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.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1007/s10955-015-1330-x
