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DTSTART:20170326T030000
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DTSTART:20161030T020000
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DTSTAMP:20260428T111848Z
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 Girko’s 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.ista.ac.at/events/338
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