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SUMMARY:Multi-Point Functional CLT for Wigner Matrices.
DTSTART:20231208T143000Z
DTEND:20231208T154500Z
DTSTAMP:20260522T144600Z
UID:indico-event-10173@indico.math.cnrs.fr
CONTACT:guillaume.barraquand@math.cnrs.fr
DESCRIPTION:Speakers: Jana Reker\n\nAbstract: Consider the random variable
  X:=Tr(f1(W)A1...fk(W)Ak)\, where W is a Hermitian Wigner matrix\, f1\,...
 \,fk are regular functions\, and A1\,...\,Ak are bounded deterministic mat
 rices. In this talk\, we study the fluctuations of X around its expectatio
 n and give a functional central limit theorem on macroscopic and mesoscopi
 c scales. Analyzing the underlying combinatorics further leads to explicit
  formulas for the variance of X as well as the covariance of X and Y:=Tr(f
 k+1(W)Ak+1...fk+ℓ(W)Ak+ℓ) of similar build. The results obtained match
  the structure of formulas in second-order free probability\, which were p
 reviously only available for fj being polynomials.\n\nhttps://indico.math.
 cnrs.fr/event/10173/
LOCATION:Salle Mirzakhani (201)
URL:https://indico.math.cnrs.fr/event/10173/
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