Spectral convergence for a general class of random matrices

By Francisco Rubio, Xavier Mestre. 2011

74 citations recorded by the source corpus.

Let be an M×N complex random matrix with i.i.d. entries having mean zero and variance 1/N and consider the class of matrices of the type , where , and are Hermitian nonnegative definite matrices, such that and have bounded spectral norm with being diagonal, and is the nonnegative definite square root of . Under some assumptions on the moments of the entries of , it is proved in this paper that, for any matrix with bounded trace norm and for each complex z outside the positive real line, almost surely as M,N-->[infinity] at the same rate, where [delta]M(z) is deterministic and solely depends on and . The previous result can be particularized to the study of the limiting behavior of the Stieltjes transform as well as the eigenvectors of the random matrix model . The study is motivated by applications in the field of statistical signal processing.

Subfields: Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/39023944f7c6b19bd8d4c1375fabdf015a114432

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Citations in the corpus

Surprises in High-Dimensional Ridgeless Least Squares Interpolation (2019, methodology): “RT sincerely thanks Edgar Dobriban for many helpful conversations about the random matrix theory literature, in particular, the literature trail leading up to Proposition 2, and the reference to Rubio and Mestre [60].”
Optimal Shrinkage-Based Portfolio Selection in High Dimensions (2016, background): “First, we present an important lemma which is a special case of Theorem 1 in Rubio and Mestre (2011).”