The outliers among the singular values of large rectangular random matrices with additive fixed rank deformation
| Main Authors: | Chapon, François, Couillet, Romain, Hachem, Walid, Mestre, Xavier |
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| Format: | Article Journal |
| Terbitan: |
, 2014
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| Subjects: | |
| Online Access: |
https://zenodo.org/record/58344 |
Daftar Isi:
- 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