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Numerical range for random matrices


Numerical range for random matrices

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dc.contributor.author Collins, Benoît pl
dc.contributor.author Gawron, Piotr pl
dc.contributor.author Litvak, Alexander E. pl
dc.contributor.author Życzkowski, Karol [SAP11011566] pl
dc.date.accessioned 2015-02-09T11:17:30Z
dc.date.available 2015-02-09T11:17:30Z
dc.date.issued 2014 pl
dc.identifier.issn 0022-247X pl
dc.identifier.uri http://ruj.uj.edu.pl/xmlui/handle/item/2908
dc.language eng pl
dc.rights Dodaję tylko opis bibliograficzny *
dc.rights.uri *
dc.title Numerical range for random matrices pl
dc.type JournalArticle pl
dc.description.physical 516-533 pl
dc.abstract.en We analyze the numerical range of high-dimensional random matrices, obtaining limit results and corresponding quantitative estimates in the non-limit case. For a large class of random matrices their numerical range is shown to converge to a disc. In particular, numerical range of complex Ginibre matrix almost surely converges to the disk of radius √2. Since the spectrum of non-hermitian random matrices from the Ginibre ensemble lives asymptotically in a neighborhood of the unit disk, it follows that the outer belt of width √2 - 1 containing no eigenvalues can be seen as a quantification the non-normality of the complex Ginibre random matrix. We also show that the numerical range of upper triangular Gaussian matrices converges to the same disk of radius √2, while all eigenvalues are equal to zero and we prove that the operator norm of such matrices converges to √2e. pl
dc.subject.en Ginibre ensemble pl
dc.subject.en Gaussian random matrix pl
dc.subject.en GUE pl
dc.subject.en numerical range pl
dc.subject.en field of values pl
dc.subject.en triangular random matrix pl
dc.description.volume 418 pl
dc.description.number 1 pl
dc.description.publication 1 pl
dc.identifier.doi 10.1016/j.jmaa.2014.03.072 pl
dc.identifier.eissn 1096-0813 pl
dc.title.journal Journal of Mathematical Analysis and Applications pl
dc.language.container eng pl
dc.affiliation Wydział Fizyki, Astronomii i Informatyki Stosowanej : Instytut Fizyki im. Mariana Smoluchowskiego pl
dc.subtype Article pl
dc.rights.original bez licencji pl
.pointsMNiSW [2014 A]: 35

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