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| HAL : hal-00692258, version 1 |
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| Electronic Journal of Probability 16, ? (2011) 1934--1959 |
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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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| Philippe Loubaton 1Pascal Vallet 1 |
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| (2011) |
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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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| 1 : | Laboratoire d'Informatique Gaspard-Monge (LIGM) |
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Université Paris-Est Marne-la-Vallée (UPEMLV) – ESIEE – Ecole des Ponts ParisTech – Fédération de Recherche Bézout – CNRS : UMR8049 |
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| Domaine | : | Mathématiques/Physique mathématique |
| hal-00692258, version 1 | |
| http://hal-upec-upem.archives-ouvertes.fr/hal-00692258 | |
| oai:hal-upec-upem.archives-ouvertes.fr:hal-00692258 | |
| Contributeur : Philippe Loubaton | |
| Déposé pour le compte de : | |
| Soumis le : Dimanche 29 Avril 2012, 16:43:10 | |
| Dernière modification le : Dimanche 29 Avril 2012, 16:43:12 | |
