Marked GUE-corners process in dimer models

by Nedialko Bradinoff (KTH)

Thursday 30 Apr 2026, 14:00 → 15:00 Europe/Brussels

B/2nd floor-B.203 - Seminar room (Marc de Hemptinne (chemin du Cyclotron, 2, Louvain-la-Neuve))

The Aztec diamond dimer model is a classical model in statistical mechanics. The Aztec diamond with uniform weights is one of the gems of integrable probability; its special structure lead to a set of remarkable local and global results in the limit as the size of the model tends to infinity. 

In recent years new tools were developed and made it possible to study the Aztec diamond with doubly periodic weights and, in great generality, at the global and local scales new limiting phenomena were proved.

In this talk I will discuss a new local limit for the Aztec diamond with certain 2 x 2 periodic weights. We study an interlacing particle system near one of  the points where the liquid disordered region touches the boundary. At this turning point under an appropriate scaling we observe a marked GUE-corners process as the size of the model grows. This is a determinantal point process obtained from the celebrated GUE-corners process by assigning independent Bernoulli marks (with location-dependent parameters) to each particle in a configuration. The proof relies on a double-contour integral representation over a certain Riemann surface of the correlation Kernel of the studied process. The talk is based on joint work with Tomas Berggren.