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Title: A statistical physics approach to the Sine beta process

Abstract: The Sine process (corresponding to inverse temperature beta equal to 2) is a determinantal point process, which is known for a long time. It appears as the bulk limit of many particle systems in various contexts (random matrix ensembles, zeros of L-functions, growth models etc.) Its universality properties are fascinating. More recently, Valko and Virag introduced the family of Sine beta processes as the bulk limit of Gaussian beta ensembles, for any positive beta. As soon as beta is different from 2, much less is known.
In a work with David Dereudre, Adrien Hardy (Universit茅 de Lille) and Thomas Lebl茅 (Universit茅 Paris Cit茅), we use tools from classical statistical mechanics based on Dobrushin-Lanford-Ruelle (DLR) equations to better understand the Sine beta process and in particular show that it is number-rigid.