File Download

There are no files associated with this item.

  Links for fulltext
     (May Require Subscription)
Supplementary

Article: On the spectral distribution of Gaussian random matrices

TitleOn the spectral distribution of Gaussian random matrices
Authors
KeywordsConvergence rate
Empirical spectral distribution
Random matrices
Wigner distribution
Issue Date2006
PublisherSpringer Verlag. The Journal's web site is located at http://link.springer.de/link/service/journals/10255/
Citation
Acta Mathematicae Applicatae Sinica, 2006, v. 22 n. 2, p. 297-312 How to Cite?
AbstractWe consider the empirical spectral distribution (ESD) of a random matrix from the Gaussian Unitary Ensemble. Based on the Plancherel-Rotach approximation formula for Hermite polynomials, we prove that the expected empirical spectral distribution converges at the rate of O(n -1) to the Wigner distribution function uniformly on every compact intervals [u, v] within the limiting support (-1, 1). Furthermore, the variance of the ESD for such an interval is proved to be (πn)-2 log n asymptotically which surprisingly enough, does not depend on the details (e. g. length or location) of the interval. This property allows us to determine completely the covariance function between the values of the ESD on two intervals. © Springer-Verlag 2006.
Persistent Identifierhttp://hdl.handle.net/10722/132619
ISSN
2015 Impact Factor: 0.25
2015 SCImago Journal Rankings: 0.220
References

 

DC FieldValueLanguage
dc.contributor.authorDelyon, Ben_HK
dc.contributor.authorYao, Jen_HK
dc.date.accessioned2011-03-28T09:27:03Z-
dc.date.available2011-03-28T09:27:03Z-
dc.date.issued2006en_HK
dc.identifier.citationActa Mathematicae Applicatae Sinica, 2006, v. 22 n. 2, p. 297-312en_HK
dc.identifier.issn0168-9673en_HK
dc.identifier.urihttp://hdl.handle.net/10722/132619-
dc.description.abstractWe consider the empirical spectral distribution (ESD) of a random matrix from the Gaussian Unitary Ensemble. Based on the Plancherel-Rotach approximation formula for Hermite polynomials, we prove that the expected empirical spectral distribution converges at the rate of O(n -1) to the Wigner distribution function uniformly on every compact intervals [u, v] within the limiting support (-1, 1). Furthermore, the variance of the ESD for such an interval is proved to be (πn)-2 log n asymptotically which surprisingly enough, does not depend on the details (e. g. length or location) of the interval. This property allows us to determine completely the covariance function between the values of the ESD on two intervals. © Springer-Verlag 2006.en_HK
dc.languageengen_US
dc.publisherSpringer Verlag. The Journal's web site is located at http://link.springer.de/link/service/journals/10255/en_HK
dc.relation.ispartofActa Mathematicae Applicatae Sinicaen_HK
dc.subjectConvergence rateen_HK
dc.subjectEmpirical spectral distributionen_HK
dc.subjectRandom matricesen_HK
dc.subjectWigner distributionen_HK
dc.titleOn the spectral distribution of Gaussian random matricesen_HK
dc.typeArticleen_HK
dc.identifier.emailYao, J: jeffyao@hku.hken_HK
dc.identifier.authorityYao, J=rp01473en_HK
dc.description.naturelink_to_subscribed_fulltexten_US
dc.identifier.doi10.1007/s10255-006-0306-7en_HK
dc.identifier.scopuseid_2-s2.0-33645661531en_HK
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-33645661531&selection=ref&src=s&origin=recordpageen_HK
dc.identifier.volume22en_HK
dc.identifier.issue2en_HK
dc.identifier.spage297en_HK
dc.identifier.epage312en_HK
dc.identifier.eissn1618-3932-
dc.publisher.placeGermanyen_HK
dc.identifier.scopusauthoridDelyon, B=6701472779en_HK
dc.identifier.scopusauthoridYao, J=7403503451en_HK

Export via OAI-PMH Interface in XML Formats


OR


Export to Other Non-XML Formats