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Almost Sure Localization of the Eigenvalues in a Gaussian Information Plus Noise Model. Application to the Spiked Models.

Dublin Core		PKP Metadata Items	Metadata for this Document
1.	Title	Title of document	Almost Sure Localization of the Eigenvalues in a Gaussian Information Plus Noise Model. Application to the Spiked Models.
2.	Creator	Author's name, affiliation, country	Philippe Loubaton; Université Paris-Est Marne-la-Vallée; France
2.	Creator	Author's name, affiliation, country	Pascal Vallet; Université Paris-Est Marne-la-Vallée; France
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	random matrix theory; gaussian information plus noise model; localization of the eigenvalues; spiked models
3.	Subject	Subject classification	15B52; 60F15
4.	Description	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.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)	This work was partially supported by the French program ANR-07-MDCO-012-01
7.	Date	(YYYY-MM-DD)	2011-10-20
8.	Type	Status & genre	Peer-reviewed Article
8.	Type	Type
9.	Format	File format	PDF
10.	Identifier	Uniform Resource Identifier	http://ejp.ejpecp.org/article/view/943
10.	Identifier	Digital Object Identifier	10.1214/EJP.v16-943
11.	Source	Journal/conference title; vol., no. (year)	Electronic Journal of Probability; Vol 16
12.	Language	English=en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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