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Matematicheskie Zametki, 2015, Volume 98, Issue 6, Pages 824–831
DOI: https://doi.org/10.4213/mzm10830 (Mi mzm10830) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Unitarily Invariant Ergodic Matrices and Free Probability

Al. I. Bufetov

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia
Full-text PDF (461 kB) Citations (1)
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DOI: https://doi.org/10.4213/mzm10830
Abstract: Probability measures on the space of Hermitian matrices which are ergodic for the conjugation action of an infinite-dimensional unitary group are considered. It is established that the eigenvalues of random matrices distributed with respect to these measures satisfy the law of large numbers. The relationship between such models of random matrices and objects in free probability, freely infinitely divisible measures, is also established.
Keywords: unitarily invariant ergodic matrix, infinitely divisible measure, free probability, Hermitian matrix, empiric distribution of eigenvalues, free convolution, free cumulant.
Funding agency Grant number
Russian Science Foundation 14-50-00005
This work was supported by the Russian Science Foundation under grant 14-50-00005.
Received: 23.09.2015
English version:
Mathematical Notes, 2015, Volume 98, Issue 6, Pages 884–890
DOI: https://doi.org/10.1134/S0001434615110206
Bibliographic databases:
Document Type: Article
UDC: 519.21
Language: Russian
Citation: Al. I. Bufetov, “Unitarily Invariant Ergodic Matrices and Free Probability”, Mat. Zametki, 98:6 (2015), 824–831; Math. Notes, 98:6 (2015), 884–890
Citation in format AMSBIB
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    • This publication is cited in the following 1 articles:
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