Jonathan Novak
Published 2014-07-28, updated 2014-12-27Version 2
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.
Comments: 9 pages, 3 figures. Version 2 fixes errors, adds clarifications and new material; title changed
A central limit theorem for products of random matrices and GOE statistics for the Anderson model on long boxes
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