01:39:42
publiée le 4 juillet 2025
Lecture 3: What is the Universal Scaling Limit of Random Interface Growth, and What Does It Tell Us?
De Ivan Corwin
Log-gases on a quadratic lattice via discrete loop equations
De Alisa Knizel
Apparaît dans la collection : Chaire Jean-Morlet : Equation intégrable aux données initiales aléatoires / Jean-Morlet Chair : Integrable Equation with Random Initial Data
We study a general class of log-gas ensembles on a quadratic lattice. Using a variational principle we prove that the corresponding empirical measures satisfy a law of large numbers and that their global fluctuations are Gaussian with a universal covariance. We apply our general results to analyze the asymptotic behavior of a q-boxed plane partition model introduced by Borodin, Gorin and Rains. In particular, we show that the global fluctuations of the height function on a fixed slice are described by a one-dimensional section of a pullback of the two-dimensional Gaussian free field. Our approach is based on a q-analogue of the Schwinger-Dyson (or loop) equations, which originate in the work of Nekrasov and his collaborators, and extends the methods developed by Borodin, Gorin and Guionnet to a quadratic lattice. Based on joint work with Evgeni Dimitrov
