Please use this identifier to cite or link to this item: https://doi.org/10.1016/j.jmva.2009.08.005
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dc.titleCircular law, extreme singular values and potential theory
dc.contributor.authorPan, G.
dc.contributor.authorZhou, W.
dc.date.accessioned2014-10-28T05:10:52Z
dc.date.available2014-10-28T05:10:52Z
dc.date.issued2010-03
dc.identifier.citationPan, G., Zhou, W. (2010-03). Circular law, extreme singular values and potential theory. Journal of Multivariate Analysis 101 (3) : 645-656. ScholarBank@NUS Repository. https://doi.org/10.1016/j.jmva.2009.08.005
dc.identifier.issn0047259X
dc.identifier.urihttp://scholarbank.nus.edu.sg/handle/10635/105055
dc.description.abstractConsider the empirical spectral distribution of complex random n × n matrix whose entries are independent and identically distributed random variables with mean zero and variance 1 / n. In this paper, via applying potential theory in the complex plane and analyzing extreme singular values, we prove that this distribution converges, with probability one, to the uniform distribution over the unit disk in the complex plane, i.e. the well known circular law, under the finite fourth moment assumption on matrix elements. © 2009 Elsevier Inc. All rights reserved.
dc.description.urihttp://libproxy1.nus.edu.sg/login?url=http://dx.doi.org/10.1016/j.jmva.2009.08.005
dc.sourceScopus
dc.subjectCircular law
dc.subjectLargest singular value
dc.subjectPotential
dc.subjectSmall ball probability
dc.subjectSmallest singular value
dc.typeArticle
dc.contributor.departmentSTATISTICS & APPLIED PROBABILITY
dc.description.doi10.1016/j.jmva.2009.08.005
dc.description.sourcetitleJournal of Multivariate Analysis
dc.description.volume101
dc.description.issue3
dc.description.page645-656
dc.description.codenJMVAA
dc.identifier.isiut000273834800013
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