lnu.sePublikationer
Ändra sökning
RefereraExporteraLänk till posten
Permanent länk

Direktlänk
Referera
Referensformat
• apa
• ieee
• modern-language-association-8th-edition
• vancouver
• Annat format
Fler format
Språk
• de-DE
• en-GB
• en-US
• fi-FI
• nn-NO
• nn-NB
• sv-SE
• Annat språk
Fler språk
Utmatningsformat
• html
• text
• asciidoc
• rtf
On the asymptotic spectral distribution of random matrices: closed form solutions using free independence
2013 (Engelska)Licentiatavhandling, monografi (Övrigt vetenskapligt)
##### Abstract [en]

The spectral distribution function of random matrices is an information-carrying object widely studied within Random matrix theory. In this thesis we combine the results of the theory together with the idea of free independence introduced by Voiculescu (1985).

Important theoretical part of the thesis consists of the introduction to Free probability theory, which justifies use of asymptotic freeness with respect to particular matrices as well as the use of Stieltjes and R-transform. Both transforms are presented together with their properties.

The aim of thesis is to point out characterizations of those classes of the matrices, which have closed form expressions for the asymptotic spectral distribution function. We consider all matrices which can be decomposed to the sum of asymptotically free independent summands.

In particular, explicit calculations are performed in order to illustrate the use of asymptotic free independence to obtain the asymptotic spectral distribution for a matrix Q and generalize Marcenko and Pastur (1967) theorem. The matrix Q is defined as

$Q = \frac{1}n X_1X^\prime_1 + \cdot\cdot\cdot + \frac{1}n X_kX^\prime_k,$

where Xi is p × n matrix following a matrix normal distribution, Xi ~ Np,n(0, \sigma^2I, I).

Finally, theorems pointing out classes of matrices Q which lead to closed formula for the asymptotic spectral distribution will be presented. Particularly, results for matrices with inverse Stieltjes transform, with respect to the composition, given by a ratio of polynomials of 1st and 2nd degree, are given.

##### Serie
Linköping studies in science and technology, ISSN 0280-7971 ; 1597
##### Nyckelord [en]
Spectral distribution, R-transform, Stieltjes transform, Free probability, Freeness, Asymptotic freeness
##### Nationell ämneskategori
Sannolikhetsteori och statistik
##### Identifikatorer
Libris ID: 14216504ISBN: 9789175195964 (tryckt)OAI: oai:DiVA.org:lnu-58181DiVA, id: diva2:1047452
##### Presentation
2013-06-03, Planck, Fysikhuset, Campus Valla, 13:15 (Engelska)

#### Open Access i DiVA

##### Filinformation
Filnamn FULLTEXT01.pdfFilstorlek 3432 kBChecksumma SHA-512
437b7443ce5c5342a3fd796b00046691367a0a6e0ddccf402919527fb7c26677fe716b46b06d2616fb261e5f117cdde9a5d2e392af171e4c7efcb329a19121d3
Typ fulltextMimetyp application/pdf

#### Person

Pielaszkiewicz, Jolanta Maria

#### Sök vidare i DiVA

##### Av författaren/redaktören
Pielaszkiewicz, Jolanta Maria
##### I ämnet
Sannolikhetsteori och statistik

#### Sök vidare utanför DiVA

Antalet nedladdningar är summan av nedladdningar för alla fulltexter. Det kan inkludera t.ex tidigare versioner som nu inte längre är tillgängliga.
isbn
urn-nbn

#### Altmetricpoäng

isbn
urn-nbn
Totalt: 129 träffar
RefereraExporteraLänk till posten
Permanent länk

Direktlänk
Referera
Referensformat
• apa
• ieee
• modern-language-association-8th-edition
• vancouver
• Annat format
Fler format
Språk
• de-DE
• en-GB
• en-US
• fi-FI
• nn-NO
• nn-NB
• sv-SE
• Annat språk
Fler språk
Utmatningsformat
• html
• text
• asciidoc
• rtf