The limiting spectral distribution of large dimensional general information-plus-noise type matrices

2022/01/28 by Zhou, Huanchao, Bai, Zhidong, Hu, Jiang · 1 citation
#FOS: Mathematics #Statistics Theory (math.ST)

paper · doi:10.48550/arxiv.2201.12079

Abstract

Let X_n be n× N random complex matrices, R_n and T_n be non-random complex matrices with dimensions n× N and n× n, respectively. We assume that the entries of X_n are independent and identically distributed, T_n are nonnegative definite Hermitian matrices and T_nR_nR_n^*= R_nR_n^*T_n . The general information-plus-noise type matrices are defined by C_n=(1)/(N)T_n^(1)/(2) ( R_n +X_n) (R_n+X_n)^*T_n^(1)/(2) . In this paper, we establish the limiting spectral distribution of the large dimensional general information-plus-noise type matrices C_n. Specifically, we show that as n and N tend to infinity proportionally, the empirical distribution of the eigenvalues of C_n converges weakly to a non-random probability distribution, which is characterized in terms of a system of equations of its Stieltjes transform.

Cited by

• No Eigenvalues Outside the Limiting Support of Generally Correlated and Noncentral Sample Covariance Matrices

Related

• Analysis of the limiting spectral distribution of large dimensional General information-plus-noise type matrices
• No Eigenvalues Outside the Support of the Limiting Spectral Distribution of Large Dimensional noncentral Sample Covariance Matrices
• Analysis of The Limiting Spectral Distribution of Large Random Matrices of The Marčenko-Pastur Type
• Analysis of the limiting spectral measure of large random matrices of the separable covariance type
• The Spectrum of Random Inner-product Kernel Matrices