Eigenvalue Density of Correlated Complex Random Wishart Matrices

Abstract

Using a character expansion method, we calculate exactly the eigenvalue density of random matrices of the form M^\dagger M where M is a complex matrix drawn from a normalized distribution P(M) ~ exp(-\Tr(A M B M^\dagger) with A and B positive definite (square) matrices of arbitrary dimensions. Such so-called ``correlated Wishart matrices'' occur in many fields ranging from information theory to multivariate analysis.

References in corpus (5)

• A Random Matrix Approach to Cross-Correlations in Financial Data
• Effective matter superpotentials from Wishart random matrices
• Generalizations of some integrals over the unitary group
• Information transfer through disordered media by diffuse waves
• Quantum-optical communication rates through an amplifying random medium

Cited by in corpus (22)

• Performance Analysis of MIMO-MRC in Double-Correlated Rayleigh Environments
• Random Matrices and the Spectrum of N-flation
• Capacity and Character Expansions: Moment generating function and other exact results for MIMO correlated channels
• Subsystem dynamics under random Hamiltonian evolution
• Eigenvalue distributions for some correlated complex sample covariance matrices
• On the Eigenvalue Density of Real and Complex Wishart Correlation Matrices
• Lyapunov exponents for products of complex Gaussian random matrices
• Random Matrix Model for Nakagami-Hoyt Fading
• Emerging spectra of singular correlation matrices under small power-map deformations
• Spectral Domain of Large Nonsymmetric Correlated Wishart Matrices
• Spectral correlation functions of the sum of two independent complex Wishart matrices with unequal covariances
• Optimal Transmit Covariance for Ergodic MIMO Channels
• Spectral density of a Wishart model for nonsymmetric Correlation Matrices
• Eigenvalue Density of the Doubly Correlated Wishart Model: Exact Results
• Eigenfunction statistics of Laguerre Brownian ensemble
• The Correlated Jacobi and the Correlated Cauchy-Lorentz ensembles
• Multivariate analysis of short time series in terms of ensembles of correlation matrices
• Localization in covariance matrices of coupled heterogenous Ornstein-Uhlenbeck processes
• Spectral density of the non-central correlated Wishart ensembles
• Exact Multivariate Amplitude Distributions for Non-Stationary Gaussian or Algebraic Fluctuations of Covariances or Correlations
• Matrix Moments in a Real, Doubly Correlated Algebraic Generalization of the Wishart Model
• Channel Eigenvalues and Effective Degrees of Freedom of Reconfigurable Intelligent Surfaces