Compound real Wishart and q-Wishart matrices

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dc.creatorBryc, Wlodek
dc.date2008-06-25
dc.date.accessioned2026-07-07T09:59:12Z
dc.date.available2026-07-07T09:59:12Z
dc.descriptionWe introduce a family of matrices with non-commutative entries that generalize the classical real Wishart matrices. With the help of the Brauer product, we derive a non-asymptotic expression for the moments of traces of monomials in such matrices; the expression is quite similar to the formula derived in our previous work for independent complex Wishart matrices. We then analyze the fluctuations about the Marchenko-Pastur law. We show that after centering by the mean, traces of real symmetric polynomials in q-Wishart matrices converge in distribution, and we identify the asymptotic law as the normal law when q=1, and as the semicircle law when q=0.
dc.identifierhttps://arxiv.org/abs/0806.4014
dc.identifierhttp://arxiv.org/abs/0806.4014
dc.identifierInt Math Res Notices (2008) Vol. 2008, article ID rnn079
dc.identifierdoi:10.1093/imrn/rnn079
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/167941
dc.subjectProbability
dc.subjectMathematical Physics
dc.subjectCombinatorics
dc.subjectOperator Algebras
dc.subjectStatistics Theory
dc.subject60G15; 15A52; 05A15; 62H05
dc.titleCompound real Wishart and q-Wishart matrices
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