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Some consequences of exchangeability in random-matrix theory

Le Caër, G. and Delannay, R. (1999) Some consequences of exchangeability in random-matrix theory. Physical Review E, 59 (6). pp. 6281-6285. ISSN 1063-651X. doi:10.1103/PhysRevE.59.6281.

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Properties of infinite sequences of exchangeable random variables result directly in explicit expressions for calculating asymptotic densities of eigenvalues ρ_∞(λ) of any ensemble of random matrices H whose distribution depends only on tr (H†H), where H† is the Hermitian conjugate of H. For real symmetric matrices and for Hermitian matrices, the densities ρ_∞(λ) are constructed by summing up Wigner semicircles with varying radii and weights as confirmed by Monte Carlo simulations. Extensions to more general matrix ensembles are also considered.

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Additional Information:© 1999 American Physical Society. (Received 14 August 1998) G.L.C. thanks the CNRS, NSF, Ministère des Affaires Etrangères, and the Division of Engineering and Applied Science (California Institute of Technology) for financial support, Professor B. Fultz and his group for their welcome, and P. Bogdanoff for a careful reading of the manuscript.
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Centre National de la Recherche Scientifique (CNRS)UNSPECIFIED
Ministère des Affaires EtrangèresUNSPECIFIED
Caltech Division of Engineering and Applied ScienceUNSPECIFIED
Issue or Number:6
Classification Code:PACS number~s!: 02.50.2r, 05.45.2a, 21.10.2k, 72.80.Ng
Record Number:CaltechAUTHORS:20170408-163845200
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:76225
Deposited By: 1Science Import
Deposited On:08 Mar 2018 23:01
Last Modified:15 Nov 2021 16:58

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