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• W2885256369 abstract "Denote by $lambda_1(A), ldots, lambda_n(A)$ the eigenvalues of an $(ntimes n)$-matrix $A$. Let $Z_n$ be an $(ntimes n)$-matrix chosen uniformly at random from the matrix analogue to the classical $ell_ p^n$-ball, defined as the set of all self-adjoint $(ntimes n)$-matrices satisfying $sum_{k=1}^n |lambda_k(A)|^pleq 1$. We prove a large deviations principle for the (random) spectral measure of the matrix $n^{1/p} Z_n$. As a consequence, we obtain that the spectral measure of $n^{1/p} Z_n$ converges weakly almost surely to a non-random limiting measure given by the Ullman distribution, as $ntoinfty$. The corresponding results for random matrices in Schatten trace classes, where eigenvalues are replaced by the singular values, are also presented." @default.
• W2885256369 created "2018-08-22" @default.
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• W2885256369 date "2018-08-14" @default.
• W2885256369 modified "2023-09-27" @default.
• W2885256369 title "Sanov-type large deviations in Schatten classes" @default.
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• W2885256369 hasPublicationYear "2018" @default.
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