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SUMMARY:Multi-Point Functional CLT for Wigner Matrices
DTSTART:20231212T085000Z
DTEND:20231212T095000Z
DTSTAMP:20240228T220300Z
UID:indico-event-11077@indico.math.cnrs.fr
DESCRIPTION:Speakers: Jana Reker\n\nConsider the random variable X:=Tr( f_
1(W)A_1 ... f_k(W)A_k)\, where W is a Hermitian Wigner matrix\, f_1\, ...
\, f_k are regular functions\, andÂ A_1\, ... \, A_k are bounded determini
stic matrices. In this talk\, we study the fluctuations of X around its ex
pectation and give a functional central limit theorem on macroscopic and m
esoscopic 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)A_{k+1} ... f_{k+\\ell}(W)A_{k+\\ell}) of similar build.
The results match the structure of formulas in second-order free probabil
ity\, previously only available for f_j being polynomials.\n\nhttps://indi
co.math.cnrs.fr/event/11077/
LOCATION:Amphi Schwartz (IMT)
URL:https://indico.math.cnrs.fr/event/11077/
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