Wigner Semicircle Law

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

Wigner Semicircle Law

Popis výsledku v původním jazyce

Wigner semicircle law is the fundamental result in the random matrix theorem. Briefly, it claims that the distribution of the mixture of the eigenvalues of a Wigner matrix converges in law to a semicircle distribution as the dimension of the matrix goesto infinity. In other words, the distribution of the mixture of corresponding eigenvalues can be approximated by a semicircle distribution for high-dimensional Wigner matrices . Such a fact could be used for example to accurately approximate unfolding based on this strong theoretical result rather than on some statistical or numerical approach which is usually used. Since the definition of Wigner matrix is satisfied by numerous kinds of random matrices, the theorem is thus pretty general and shows the power and universality of eigenvalues of large random matrices. Even thought the theorem describes one of the basic properties of random eigenvalues, its proof is on the other hand quite long and demanding. Some advanced results from diffe

Název v anglickém jazyce

Wigner Semicircle Law

Popis výsledku anglicky

Wigner semicircle law is the fundamental result in the random matrix theorem. Briefly, it claims that the distribution of the mixture of the eigenvalues of a Wigner matrix converges in law to a semicircle distribution as the dimension of the matrix goesto infinity. In other words, the distribution of the mixture of corresponding eigenvalues can be approximated by a semicircle distribution for high-dimensional Wigner matrices . Such a fact could be used for example to accurately approximate unfolding based on this strong theoretical result rather than on some statistical or numerical approach which is usually used. Since the definition of Wigner matrix is satisfied by numerous kinds of random matrices, the theorem is thus pretty general and shows the power and universality of eigenvalues of large random matrices. Even thought the theorem describes one of the basic properties of random eigenvalues, its proof is on the other hand quite long and demanding. Some advanced results from diffe

Druh

D - Stať ve sborníku

CEP obor

BE - Teoretická fyzika

OECD FORD obor

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Projekt

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Návaznosti

S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2015

Kód důvěrnosti údajů

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

Název statě ve sborníku

SPMS 2015 - Stochastic and Physical Monitoring Systems - Proceedings

ISBN

978-80-01-05841-1

ISSN

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e-ISSN

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Počet stran výsledku

7

Strana od-do

81-87

Název nakladatele

ČVUT

Místo vydání

Praha

Místo konání akce

Drhleny

Datum konání akce

22. 6. 2015

Typ akce podle státní příslušnosti

EUR - Evropská akce

Kód UT WoS článku

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