Random Lozenge Waterfall

Leonid Petrov (U Virginia)

Oct 01. 2026, 09:30 — 10:30

Uniformly random lozenge tilings of large domains are locally described by two-dimensional translation-invariant Gibbs measures, with Gaussian Free Field fluctuations and Airy processes at the edges. I will discuss the q-Racah measure on tilings of a hexagon in the regime where q stays fixed instead of tending to 1. This is a strong double-well potential along one lattice direction. It produces a new macroscopic phase, the waterfall, in which the two-dimensional Gibbs structure collapses into a one-dimensional random interface, the barcode. We prove a law of large numbers for the waterfall profile and describe an explicit correlation kernel for the barcode, which is invariant under shifts by 2 but not by 1. Based on joint works with Alisa Knizel and Yizhen Li.

Further Information
Venue:
ESI Boltzmann Lecture Hall
Associated Event:
Statistical Mechanics and Combinatorics of Discrete Planar Structures (Thematic Programme)
Organizer(s):
Nathanael Berestycki (U of Vienna)
Michael Drmota (TU Wien)
Ilse Fischer (U of Vienna)
Mihyun Kang (TU Graz)
Astrid Kollros (U of Vienna)
Christian Krattenthaler (U of Vienna)
Marcin Lis (TU Wien)
Benedikt Stufler (TU Wien)
Fabio Toninelli (TU Wien)