The Outliers among the Singular Values of Large Rectangular Random Matrices with Additive Fixed Rank Deformation

Abstract

Consider the matrix Σn = nXnD 1/2 n + Pn where the matrix Xn ∈ CN×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 nXnDnX n both converge towards a compactly supported probability measure μ as N, n… (More)

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