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Article: On the convergence of the spectral empirical process of Wigner matrices

TitleOn the convergence of the spectral empirical process of Wigner matrices
Authors
KeywordsCentral limit theorem
Linear spectral statistics
Random matrix
Spectral distribution
Wigner matrices
Issue Date2005
PublisherInternational Statistical Institute. The Journal's web site is located at http://www.cbs.nl/isi/bernoulli/INDEX.HTM
Citation
Bernoulli, 2005, v. 11 n. 6, p. 1059-1092 How to Cite?
AbstractIt is well known that the spectral distribution Fn of a Wigner matrix converges to Wigner's semicircle law. We consider the empirical process indexed by a set of functions analytic on an open domain of the complex plane including the support of the semicircle law. Under fourth-moment conditions, we prove that this empirical process converges to a Gaussian process. Explicit formulae for the mean function and the covariance function of the limit process are provided. © 2005 ISI/BS.
Persistent Identifierhttp://hdl.handle.net/10722/132621
ISSN
2015 Impact Factor: 1.372
2015 SCImago Journal Rankings: 2.120
ISI Accession Number ID
References

 

DC FieldValueLanguage
dc.contributor.authorBai, ZDen_HK
dc.contributor.authorYao, Jen_HK
dc.date.accessioned2011-03-28T09:27:03Z-
dc.date.available2011-03-28T09:27:03Z-
dc.date.issued2005en_HK
dc.identifier.citationBernoulli, 2005, v. 11 n. 6, p. 1059-1092en_HK
dc.identifier.issn1350-7265en_HK
dc.identifier.urihttp://hdl.handle.net/10722/132621-
dc.description.abstractIt is well known that the spectral distribution Fn of a Wigner matrix converges to Wigner's semicircle law. We consider the empirical process indexed by a set of functions analytic on an open domain of the complex plane including the support of the semicircle law. Under fourth-moment conditions, we prove that this empirical process converges to a Gaussian process. Explicit formulae for the mean function and the covariance function of the limit process are provided. © 2005 ISI/BS.en_HK
dc.languageengen_US
dc.publisherInternational Statistical Institute. The Journal's web site is located at http://www.cbs.nl/isi/bernoulli/INDEX.HTMen_HK
dc.relation.ispartofBernoullien_HK
dc.subjectCentral limit theoremen_HK
dc.subjectLinear spectral statisticsen_HK
dc.subjectRandom matrixen_HK
dc.subjectSpectral distributionen_HK
dc.subjectWigner matricesen_HK
dc.titleOn the convergence of the spectral empirical process of Wigner 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.doi10.3150/bj/1137421640en_HK
dc.identifier.scopuseid_2-s2.0-33645671934en_HK
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-33645671934&selection=ref&src=s&origin=recordpageen_HK
dc.identifier.volume11en_HK
dc.identifier.issue6en_HK
dc.identifier.spage1059en_HK
dc.identifier.epage1092en_HK
dc.identifier.isiWOS:000234394700006-
dc.publisher.placeNetherlandsen_HK
dc.identifier.scopusauthoridBai, ZD=7202524223en_HK
dc.identifier.scopusauthoridYao, J=7403503451en_HK

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