A Statistical Physics Approach to the Sine Beta Process and Other Random Point Processes

Explore a 54-minute lecture on the statistical physics approach to the Sine Beta Process and other random point processes. Delve into the ubiquitous Sine process, its appearance as the bulk limit in various particle systems, and its fascinating universality properties. Learn about the family of Sine beta processes introduced by Valko and Virag, and discover how tools from classical statistical mechanics, such as Dobrushin-Lanford-Ruelle (DLR), can be applied to better understand their structure. Examine the joint work of Mylène Maïda, David Dereudre, Adrien Hardy, and Thomas Leblé, while also reviewing other recent applications in this field. Gain insights into the complexities of these processes, particularly when the inverse temperature beta differs from 2, and broaden your understanding of random matrix ensembles, zeros of L-functions, and growth models.