Some consequences of exchangeability in random-matrix theory.
Properties of infinite sequences of exchangeable random variables result directly in explicit expressions for calculating asymptotic densities of eigenvalues rho(infinity)(lambda) 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 rho(infinity)(lambda) 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.
Le Caër
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Division of Engineering and Applied Science, Mail Stop 138-78, California Institute of Technology, Pasadena, CA 91125, USA. lecaer@mines.u-nancy.fr
Delannay
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