How to See the Tracy-Widom Distribution in the 3D Ising Model
Time: 2022-12-08
Published By: Wenqiong Li
Speaker(s): Senya Shlosman (Skoltech, Russia & Center de Physique Theorique in Marseille, France)
Time: 14:00-15:00 December 13, 2022
Venue: Online
Abstract: I will start with a reminder about the Ising model, the simplest example of a Markov random field. Then I will talk about the formation of the crystals in the 3D Ising model. At low temperatures, such a crystal has flat facets. I will argue that the fluctuations of the boundary of the top layer of the crystal of size N are not the usual N^{1/2} Gaussian fluctuations; rather they are of the order of N^{1/3}. If scaled properly, the distribution of these fluctuations converge to the Tracy-Widom distribution, which appeared earlier in the study of the spectrum of random matrices.
Joint work with Patrik Ferrari, arXiv:2209.14047
Speaker: Senya Shlosman is a Professor of Mathematics at Skoltech, Russia, and an emeritus Professor at the Center de Physique Theorique in Marseille, France. He studied math. at Moscow State University and got his Ph.D. under the supervision of Prof. Roland Dobrushin. After spending several years at UC Irvine he moved to Centre de Physique Theorique, Marseille. Five years ago he joined the Center of Advanced Studies at Skoltech. His research interests include rigorous statistical mechanics and the theory of phase transitions. Together with R. Dobrushin and R. Kotecky, he coauthored the book on the Wulf construction. He is also working in topology and combinatorics. Outside mathematics his main attractors are the music of J.S. Bach and the piano performance by Grigory Sokolov.
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