Analysis of the limiting spectral distribution of large dimensional General information-plus-noise type matrices

2023/02/03 by Huanchao Zhou, Jiang Hu, Zhou, Huanchao +5 · 1 citation
Mathematics · Computer Science · Physics and Astronomy · #Random Matrices and Applications #Blind Source Separation Techniques #Quantum optics and atomic interactions

paper · pdf · doi:10.48550/arxiv.2302.01711

Abstract

In this paper, we derive the analytical behavior of the limiting spectral distribution of non-central covariance matrices of the "general information-plus-noise" type, as studied in [14]. Through the equation defining its Stieltjes transform, it is shown that the limiting distribution has a continuous derivative away from zero, the derivative being analytic wherever it is positive, and we show the determination criterion for its support. We also extend the result in [14] to allow for all possible ratios of row to column of the underlying random matrix.

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