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TZID:Europe/Vienna
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DTSTART:20180325T030000
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TZOFFSETTO:+0200
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DTSTART:20181028T020000
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DTSTAMP:20230327T163440Z
UID:59c8cedc49a2f093347706@ist.ac.at
DTSTART:20181002T160000
DTEND:20181002T180000
DESCRIPTION:Speaker: Yuriy Nemish\nhosted by Laszlo Erdös\nAbstract: Under
some numerically checkable conditions\, we establish the optimal local la
w\, i.e.\, we show that the empirical spectral distribution on scales just
above the eigenvalue spacing follows the global density of states which i
s determined by free probability theory. First\, we give a brief introduct
ion to the linearization technique that allows to transform the polynomial
model into a linear one\, which has simpler correlation structure but hig
her dimension. After that we show that the local law holds up to the optim
al scale for the generalized resolvent of the linearized model\, which als
o yields the local law for polynomials. Finally\, we show how the above re
sults can be applied to prove the optimal bulk local law for two concrete
families of polynomials: general quadratic forms in Wigner matrices and sy
mmetrized products of independent matrices with i.i.d. entries.This is a j
oint work with Laszlo Erdös and Torben Krüger .
LOCATION:Big Seminar room Ground floor / Office Bldg West (I21.EG.101)\, IS
TA
ORGANIZER:jdeanton@ist.ac.at
SUMMARY:Yuriy Nemish: Local laws for polynomials of Wigner matrices
URL:https://talks-calendar.ista.ac.at/events/1408
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