Limiting Spectral Distributions of Random Matrices Having Equi-Correlated Normal Structure
Abstract
By rank inequalities, we show that the limiting spectral distribution of random matrices, which are Fisher matrices and Beta matrices composed of two independent samples from independent p-dimensional, centered normal populations such that all entries have unit variance and any correlation coefficient between different variables are fixed nonnegative r1, r2 < 1. Moreover, by similar method, we also present the limiting spectral distribution of Wigner matrices, Toeplitz matrices, and Hankel matrices of order p, where all entries are standard normal random variables and mutually correlated with a fixed nonnegative r < 1. However, the rank inequality for empirical spectral distributions is unable to show the limiting spectral distributions of Markov matrices and banded Toeplitz matrices because the perturbation matrices of those matrices have a rate rank 1.
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