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Recursive formula for E(∏i Tr{(WΣ-1)mi}), where W~Wp(∑; n) in finite and asymptotic regime
Linköping University, Department of Mathematics, Mathematical Statistics . Linköping University, The Institute of Technology.
Linköping University, Department of Mathematics, Mathematical Statistics . Linköping University, The Institute of Technology. Department of Energy and Technology, Swedish University of Agricultural Sciences, SE-750 07 Uppsala, Sweden..
Linköping University, Department of Mathematics, Mathematical Statistics . Linköping University, The Institute of Technology.ORCID iD: 0000-0001-9896-4438
2015 (English)Report (Other academic)
Abstract [en]

In this paper, we give a general recursive formula for E(∏i Tr{(WΣ-1)mi}), where W~Wp(∑; n) denotes a real Wishart matrix. Formulas for xed n; p are presented as well as asymptotic versions when n/p→c, when n,p→∞ i.e., when the so called Kolmogorov condition holds. Finally, we show application of the asymptotic moment relation when deriving moments for the Marchenko-Pastur distribution (free Poisson law). A numerical illustration using implementation of the main result is also performed.

Place, publisher, year, edition, pages
Linköping University Electronic Press, 2015. , 25 p.
Series
LiTH-MAT-R, ISSN 0348-2960 ; 2015:04
Keyword [en]
Wishart matrix; spectral distribution; eigenvalue distribution; moments;random matrices; free Poisson law; Marchenko-Pastur law.
National Category
Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-114277ISRN: LiTH-MAT-R--2015/04--SEOAI: oai:DiVA.org:liu-114277DiVA: diva2:788775
Available from: 2015-02-16 Created: 2015-02-16 Last updated: 2015-02-16

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Recursive formula for E(∏i Tr{(WΣ-1)mi}), where W~Wp(∑; n) in finite and asymptotic regime(1317 kB)266 downloads
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Pielaszkiewicz, Jolantavon Rosen, DietrichSingull, Martin

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CiteExportLink to record
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Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
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  • Other style
More styles
Language
  • de-DE
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  • nn-NB
  • sv-SE
  • Other locale
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Output format
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