Random tilings and Nekrasov's equations (Alice Guionnet, ENS Lyon)

23.02.2026 16:15 – 18:00

Abstract:
We will discuss this limit shape of random tilings and their fluctuations around it, for general domains that do not need to be simply connected. In particular, we show that the Kenyon-Okounkov conjecture that these fluctuations are described by a Gaussian Free Field is valid for a wide variety of models. Because of their strong constraints, random tiles can be considered as strongly interacting random variables.
Their analysis is closely related with that of the spectrum of random matrices and the so called Beta-ensembles or Coulomb gases. In this talk, we will introduce discrete Beta-ensembles and their specialization to lozenge tilings, and explain how to use a system of equations introduced by Nekrasov to study them. This talk is based on joint works with Alexei Borodin, Gaetan Borot and Vadim Gorin.

Lieu

Bâtiment: Conseil Général 7-9

Room 1-15, Séminaire Math Physics

entrée libre