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DTSTART:20170326T030000
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DTSTART:20161030T020000
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DTSTAMP:20220817T005724Z
UID:57f791caf1441860929376@ist.ac.at
DTSTART:20170309T160000
DTEND:20170309T180000
DESCRIPTION:Speaker: Johannes Alt\nhosted by Laszlo Erdös\nAbstract: The d
ensity of eigenvalues of large random matrices typically converges to a de
terministic limit as the dimension of the matrix tends to infinity. In the
Hermitian case\, the best known examples are the Wigner semicircle law fo
r Wigner ensembles and the Marchenko-Pastur law for sample covariance matr
ices. In the non-Hermitian case\, the most prominent result is Girkos ci
rcular law: The eigenvalue distribution of a matrix X with centered\, inde
pendent entries converges to a limiting density supported on a disk. Altho
ugh inhomogeneous in general\, the density is uniform for identical varian
ces. In this special case\, the local circular law by Bourgade et. al. sho
ws this convergence even locally on scales slightly above the typical eige
nvalue spacing. In the general case\, the density is obtained via solving
a system of deterministic equations. In my talk\, I explain how a detailed
stability analysis of these equations yields the local inhomogeneous circ
ular law in the bulk spectrum for a general variance profile of the entrie
s of X. This result was obtained in joint work with László Erdös and To
rben Krüger.\n
LOCATION:Seminar room Big Ground floor / Office Bldg West (I21.EG.101)\, IS
TA
ORGANIZER:jdeanton@ist.ac.at
SUMMARY:Johannes Alt: Local inhomogeneous circular law
URL:https://talks-calendar.app.ist.ac.at/events/338
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