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2011 Almost Sure Localization of the Eigenvalues in a Gaussian Information Plus Noise Model. Application to the Spiked Models.
Philippe Loubaton, Pascal Vallet
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Electron. J. Probab. 16: 1934-1959 (2011). DOI: 10.1214/EJP.v16-943

Abstract

Let $S$ be a $M$ times $N$ random matrix defined by $S = B + \sigma W$ where $B$ is a uniformly bounded deterministic matrix and where $W$ 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 of the Gram matrix $SS^*$ when $M$ and $N$ converge to infinity such that the ratio $M/N$ converges towards a constant $c > 0$. The results are used in order to derive, using an alternative approach, known results concerning the behavior of the largest eigenvalues of $SS^*$ when the rank of $B$ remains fixed and $M$ and $N$ converge to infinity.

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Philippe Loubaton. Pascal Vallet. "Almost Sure Localization of the Eigenvalues in a Gaussian Information Plus Noise Model. Application to the Spiked Models.." Electron. J. Probab. 16 1934 - 1959, 2011. https://doi.org/10.1214/EJP.v16-943

Information

Accepted: 20 October 2011; Published: 2011
First available in Project Euclid: 1 June 2016

zbMATH: 1245.15039
MathSciNet: MR2851051
Digital Object Identifier: 10.1214/EJP.v16-943

Subjects:
Primary: 15B52
Secondary: 60F15

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Vol.16 • 2011
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