Student Probability Seminar

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Optimal local laws and CLT for 1D Riesz gases

Speaker: Jeanne Boursier, Université Paris-Dauphine

Location: Warren Weaver Hall 517

Date: Monday, December 13, 2021, 11:30 a.m.

Synopsis:

I will present results concerning the fluctuations of one-dimensional gasses of classical particles with long-range Riesz interaction. Combining loop equation techniques, concentration inequalities and tools from the analysis of Helffer-Sjöstrand equations, we can obtain a Central Limit Theorem for linear statistics allowing for singular test-functions. I will introduce – in a rather informal way – the idea of Hellfer-Sjöstrand representation and the associated maximum principle, which is a key ingredient in our proof.