Lozenge tilings and Hurwitz numbers

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.

9 pages, 3 figures. Version 2 fixes errors, adds clarifications and new material; title changed

Cited by in corpus (9)

• Fluctuations of particle systems determined by Schur generating functions
• Bulk universality for random lozenge tilings near straight boundaries and for tensor products
• On the Complex Asymptotics of the HCIZ and BGW Integrals
• Tilings of non-convex Polygons, skew-Young Tableaux and determinantal Processes
• Lozenge tilings of hexagons with cuts and asymptotic fluctuations: a new universality class
• Double Interlacing in Random Tiling Models
• Correlations in totally symmetric self-complementary plane partitions
• On the convergence of monotone Hurwitz generating functions
• Hidden symmetries of weighted lozenge tilings