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SUMMARY:Laszlo Erdös (IST Austria)
DTSTART:20210211T160000Z
DTEND:20210211T173000Z
DTSTAMP:20260423T021303Z
UID:AQFP/7
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/AQFP/7/">Eig
 enstate thermalisation hypothesis and functional CLT for Wigner matrices</
 a>\nby Laszlo Erdös (IST Austria) as part of Analysis\, Quantum Fields\, 
 and Probability\n\n\nAbstract\nWe prove  that any deterministic matrix is 
 approximately the identity in the eigenbasis of a large random Wigner matr
 ix W with an optimal error inversely proportional to the square root of th
 e dimension. This verifies a strong form of  Quantum Unique Ergodicity wit
 h an optimal convergence rate and we also prove Gaussian fluctuations arou
 nd this convergence after a small spectral averaging. This requires to ext
 end the classical CLT for linear eigenvalue statistics\, Tr f(W)\, to incl
 ude a deterministic matrix A  and  we identify three different modes of fl
 uctuation for Tr f(W)A in the entire mesoscpic regime. The key technical t
 ool is a new multi-resolvent local law for Wigner ensemble.\n
LOCATION:https://researchseminars.org/talk/AQFP/7/
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