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SUMMARY:Michel Pain (New York University)
DTSTART:20210409T120000Z
DTEND:20210409T130000Z
DTSTAMP:20260423T005729Z
UID:MEGA/24
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MEGA/24/">Op
 timal local law and central limit theorem for beta-ensembles.</a>\nby Mich
 el Pain (New York University) as part of Séminaire MEGA\n\n\nAbstract\nIn
  this talk\, I will present a joint work with Paul Bourgade and Krishnan M
 ody. We consider beta-ensembles with general potentials (or equivalently a
  log-gas in dimension 1)\, which are a generalization of Gaussian beta-ens
 embles and of classical invariant ensembles of random matrices. We prove a
  multivariate central limit theorem for the logarithm of the characteristi
 c polynomial\, showing that it behaves as a log-correlated field. A key in
 gredient is an optimally sharp local law for the the Stieljes transform of
  the empirical measure which can be of independent interest. Both the proo
 fs of the CLT and the local law are based essentially on loop equations te
 chniques.\n
LOCATION:https://researchseminars.org/talk/MEGA/24/
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