| Type de publication : |
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Articles dans des revues avec comité de lecture |
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| Domaine : |
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Mathématiques/Physique mathématique
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| Titre : |
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Almost sure localization of the eigenvalues in a Gaussian information plus noise model - Application to the spiked models |
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| Auteur(s) : |
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Philippe Loubaton 1, Pascal Vallet 1 |
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| Laboratoire : |
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| Résumé : |
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Let Sigma(N) be a M x N random matrix defined by Sigma(N) = B(N) + sigma W(N) where B(N) is a uniformly bounded deterministic matrix and where W(N) is an independent identically distributed complex Gaussian matrix with zero mean and variance 1/N entries. The purpose of this paper is to study the almost sure location of the eigenvalues (lambda) over cap (1,N) >= ... >= (lambda) over cap (M,N) of the Gram matrix Sigma(N)Sigma(N)* when M and N converge to +infinity such that the ratio c(N) = M/N converges towards a constant c > 0. The results are used in order to derive, using an alternative approach, known results concerning the behaviour of the largest eigenvalues of Sigma(N)Sigma(N)* when the rank of B(N) remains fixed and M, N tend to +infinity. |
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Langue du texte
intégral : |
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Anglais |
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| Journal : |
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| Audience : |
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internationale |
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| Date de publication : |
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2011 |
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| Volume : |
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16 |
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| Numéro : |
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? |
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| Page, identifiant, ... : |
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1934--1959 |
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