Wigner Semicircle Law

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F15%3A00236283" target="_blank" >RIV/68407700:21340/15:00236283 - isvavai.cz</a>
Result on the web
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DOI - Digital Object Identifier
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Result language
angličtina
Original language name
Wigner Semicircle Law
Original language description
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
Czech name
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Czech description
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Publication year
2015
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Article name in the collection
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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Number of pages
7
Pages from-to
81-87
Publisher name
ČVUT
Place of publication
Praha
Event location
Drhleny
Event date
Jun 22, 2015
Type of event by nationality
EUR - Evropská akce
UT code for WoS article
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