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DTSTART:20210328T030000
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DTSTAMP:20260403T220814Z
UID:1632405600@ist.ac.at
DTSTART:20210923T160000
DTEND:20210923T165000
DESCRIPTION:Speaker: Yuanyuan Xu\nhosted by Laszlo Erdös\nAbstract: In thi
 s talk\, we will discuss the quantitative Tracy-Widom law for the largest 
 eigenvalue of Wigner matrices\, as well as sample covariance matrices.  M
 ore precisely\, we will prove that the fluctuations of the largest eigenva
 lue of a Wigner matrix of size N converge to its Tracy-Widom limit at a ra
 te nearly N^{-1/3}\, as N tends to infinity.  Our result follows from a q
 uantitative Green function comparison theorem\, originally introduced by E
 rdos\, Yau and Yin to prove edge universality\, on a finer spectral parame
 ter scale with improved error estimates. The proof relies on the continuou
 s Green function flow induced by a matrix-valued Ornstein-Uhlenbeck proces
 s. Precise estimates on leading contributions from the third and fourth or
 der moments of the matrix entries are obtained using iterative cumulant ex
 pansions and recursive comparisons for correlation functions\, along with 
 uniform convergence estimates for correlation kernels of the Gaussian ense
 mbles. This is joint work with Kevin Schnelli.
LOCATION:Heinzel Seminar Room\, Office Building West\, Ground floor\, ISTA
ORGANIZER:birgit.oosthuizen-noczil@ist.ac.at
SUMMARY:Yuanyuan Xu: Quantitative Tracy-Widom law for Wigner matrices
URL:https://talks-calendar.ista.ac.at/events/3251
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