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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
Bai, ZDYao, J
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?
DOI: http://dx.doi.org/10.3150/bj/1137421640
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
1350-7265
2021 Impact Factor: 1.822
2020 SCImago Journal Rankings: 1.814
ISI Accession Number ID
WOS:000234394700006
References
References in Scopus

 

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
dc.identifier.issnl1350-7265-

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