Analysis of the Limiting Spectral Distribution of Large-dimensional General Information-Plus-Noise-Type Matrices

Huanchao Zhou, Jiang Hu (), Zhidong Bai and Jack W. Silverstein
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Huanchao Zhou: Northeast Normal University
Jiang Hu: Northeast Normal University
Zhidong Bai: Northeast Normal University
Jack W. Silverstein: North Carolina State University

Journal of Theoretical Probability, 2024, vol. 37, issue 2, 1199-1229

Abstract: 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 Zhou (JTP 36:1203–1226, 2023). 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 Zhou (JTP 36:1203-1226, 2023) to allow for all possible ratios of row to column of the underlying random matrix.

Keywords: Random matrix; Limiting spectral distribution; Stieltjes transform; Information-plus-noise matrix; 60B20; 62H10 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10959-023-01276-3

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