Random tilings and Nekrasov's equations
| Quand ? |
Le 15/06/2026, de 10:45 à 11:45 |
|---|---|
| Où ? | Salle Condorcet |
| S'adresser à | Etera Livine |
| Participants |
Alice Guionnet |
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How does a lozenge tiling of a given domain taken at random typically looks like when the number of tiles goes to infinity ? We will discuss its limit shape and fluctuations around it, for general domains that do not need to be simply connected. In particular, we show that the Kenyon-Okounkov conjecture is valid for a wide variety of domains. 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, Gaëtan Borot and Vadim Gorin.