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Probability and Combinatorics

Tuesday, September 11, 2018 - 3:00pm

Thomas Leblé

NYU

Location

Temple University

Wachman Hall 617

Note the location change

One-dimensional log-gases, or Beta-ensembles, are statistical physics toy models finding their incarnation in random matrix theory. Their limit behavior at microscopic scale is known as the Sine-beta process, its original description involves systems of coupled SDE’s. 
We give a new description of Sine-beta as an « infinite volume Gibbs measure », using the Dobrushin-Lanford-Ruelle (DLR) formalism, and use it to prove the “rigidity” of the process, in the sense of Ghosh-Peres. If time permits, I will mention another application to the study of fluctuations of linear statistics. Joint work with David Dereudre, Adrien Hardy, and Mylène Maïda.