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

DOI10.1007/S10959-023-01276-3arXiv2302.01711MaRDI QIDQ6425334

Huanchao Zhou, Jack W. Silverstein, Zhidong Bai, Jiang Hu

Publication date: 3 February 2023

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.

Mathematics Subject Classification ID

Multivariate distribution of statistics (62H10) Random matrices (probabilistic aspects) (60B20)

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