# The outliers among the singular values of large rectangular random matrices with additive fixed rank deformation

Abstract : Consider the matrix Σn=n−1/2XnD1/2n+Pn where the matrix $X_n \in \C^{N\times n}$ has Gaussian standard independent elements, Dn is a deterministic diagonal nonnegative matrix, and Pn is a deterministic matrix with fixed rank. Under some known conditions, the spectral measures of ΣnΣ∗n and n−1XnDnX∗n both converge towards a compactly supported probability measure μ as N,n→∞ with N/n→c>0. In this paper, it is proved that finitely many eigenvalues of ΣnΣ∗n may stay away from the support of μ in the large dimensional regime. The existence and locations of these outliers in any connected component of $\R - \support(\mu)$ are studied. The fluctuations of the largest outliers of ΣnΣ∗n are also analyzed. The results find applications in the fields of signal processing and radio communications.
Type de document :
Article dans une revue
Markov Processes and Related Fields, Polymath, 2014, 20 (2), pp.183-228
Domaine :

https://hal-supelec.archives-ouvertes.fr/hal-01084173
Contributeur : Catherine Magnet <>
Soumis le : mardi 18 novembre 2014 - 16:23:38
Dernière modification le : jeudi 11 janvier 2018 - 06:23:39

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• HAL Id : hal-01084173, version 1

### Citation

François Chapon, Romain Couillet, Walid Hachem, Xavier Mestre. The outliers among the singular values of large rectangular random matrices with additive fixed rank deformation. Markov Processes and Related Fields, Polymath, 2014, 20 (2), pp.183-228. 〈hal-01084173〉

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