BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Michel Pain (NYU Courant) DTSTART:20210129T173000Z DTEND:20210129T183000Z DTSTAMP:20260423T024555Z UID:PatC/25 DESCRIPTION:Title: Op timal local law and central limit theorem for beta-ensembles\nby Miche l Pain (NYU Courant) as part of Probability and the City Seminar\n\n\nAbst ract\nIn this talk\, I will present a joint work with Paul Bourgade and Kr ishnan Mody. We consider beta-ensembles with general potentials (or equiva lently a log-gas in dimension 1)\, which are a generalization of Gaussian beta-ensembles and of classical invariant ensembles of random matrices. We prove a multivariate central limit theorem for the logarithm of the chara cteristic polynomial\, showing that it behaves as a log-correlated field. A key ingredient is an optimally sharp local law for the the Stieljes tran sform of the empirical measure which can be of independent interest. Both the proofs of the CLT and the local law are based essentially on loop equa tions techniques.\n LOCATION:https://researchseminars.org/talk/PatC/25/ END:VEVENT END:VCALENDAR