Spectral properties of non-gaussian random matrices

Kód výsledku v IS VaVaI

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Výsledek na webu

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DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

Spectral properties of non-gaussian random matrices

Popis výsledku v původním jazyce

The main topic of this article is spectral analysis of random matrices. It is well known that distribution of normalized eigenvalues of general and real gaussian matrices is de- scribed by the Girko's circle law, i.e. eigenvalues of matrix lie inside ofunit circle centered to origin of the complex plain. If the random matrix is symmetrical the distribution of eigenval- ues is described by Wigner's semicircle law. Furthermore, the so-called spacing distribution is investigated. This variable is random and its distribution is described by Izrailev's formula. Generalizations of these laws for non-gaussian matrices are introduced. Numerical tests (imple- mented in MATLAB) have shown that properties of eigenvalues of real non-gaussian matrices are in°uenced by variance of elements of matrix only and they are independent of their distribution. The mentioned tests were executed for matrices with elements chosen from uniform, Poissonian and gamma distribution. Moreover, the hypothesis about g

Název v anglickém jazyce

Spectral properties of non-gaussian random matrices

Popis výsledku anglicky

The main topic of this article is spectral analysis of random matrices. It is well known that distribution of normalized eigenvalues of general and real gaussian matrices is de- scribed by the Girko's circle law, i.e. eigenvalues of matrix lie inside ofunit circle centered to origin of the complex plain. If the random matrix is symmetrical the distribution of eigenval- ues is described by Wigner's semicircle law. Furthermore, the so-called spacing distribution is investigated. This variable is random and its distribution is described by Izrailev's formula. Generalizations of these laws for non-gaussian matrices are introduced. Numerical tests (imple- mented in MATLAB) have shown that properties of eigenvalues of real non-gaussian matrices are in°uenced by variance of elements of matrix only and they are independent of their distribution. The mentioned tests were executed for matrices with elements chosen from uniform, Poissonian and gamma distribution. Moreover, the hypothesis about g

Druh

D - Stať ve sborníku

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

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Návaznosti

S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2010

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název statě ve sborníku

SPMS 2010 Stochastic and Physical Monitoring Systems

ISBN

978-80-01-04641-8

ISSN

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e-ISSN

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Počet stran výsledku

12

Strana od-do

1-12

Název nakladatele

ČVUT

Místo vydání

Praha

Místo konání akce

Děčín

Datum konání akce

27. 6. 2010

Typ akce podle státní příslušnosti

EUR - Evropská akce

Kód UT WoS článku

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