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Spectral relations between products and powers of isotropic random matrices
We show that the limiting eigenvalue density of the product of n identically distributed random matrices from an isotropic unitary ensemble is equal to the eigenvalue density of nth power of a single matrix from this ensemble, in the limit when the size of the matrix tends to infinity. Using this observation, one can derive the limiting density of the product of n independent identically distributed non-Hermitian matrices with unitary invariant measures. In this paper we discuss two examples: the product of n Girko-Ginibre matrices and the product of n truncated unitary matrices. We also provide evidence that the result holds also for isotropic orthogonal ensembles.
cris.lastimport.wos | 2024-04-09T20:46:07Z | |
dc.abstract.en | We show that the limiting eigenvalue density of the product of n identically distributed random matrices from an isotropic unitary ensemble is equal to the eigenvalue density of nth power of a single matrix from this ensemble, in the limit when the size of the matrix tends to infinity. Using this observation, one can derive the limiting density of the product of n independent identically distributed non-Hermitian matrices with unitary invariant measures. In this paper we discuss two examples: the product of n Girko-Ginibre matrices and the product of n truncated unitary matrices. We also provide evidence that the result holds also for isotropic orthogonal ensembles. | pl |
dc.affiliation | Wydział Fizyki, Astronomii i Informatyki Stosowanej : Instytut Fizyki im. Mariana Smoluchowskiego | pl |
dc.contributor.author | Burda, Zdzisław - 127492 | pl |
dc.contributor.author | Nowak, Maciej - 131031 | pl |
dc.contributor.author | Swiech, A. | pl |
dc.date.accessioned | 2016-05-10T12:22:05Z | |
dc.date.available | 2016-05-10T12:22:05Z | |
dc.date.issued | 2012 | pl |
dc.description.number | 6 | pl |
dc.description.publication | 0,4 | pl |
dc.description.volume | 86 | pl |
dc.identifier.articleid | 061137 | pl |
dc.identifier.doi | 10.1103/PhysRevE.86.061137 | pl |
dc.identifier.eissn | 1550-2376 | pl |
dc.identifier.issn | 1539-3755 | pl |
dc.identifier.uri | http://ruj.uj.edu.pl/xmlui/handle/item/25322 | |
dc.language | eng | pl |
dc.language.container | eng | pl |
dc.rights | Dodaję tylko opis bibliograficzny | * |
dc.rights.licence | bez licencji | |
dc.rights.uri | * | |
dc.subtype | Article | pl |
dc.title | Spectral relations between products and powers of isotropic random matrices | pl |
dc.title.journal | Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics | pl |
dc.type | JournalArticle | pl |
dspace.entity.type | Publication |