Eigenvalue Density of Correlated Complex Random Wishart Matrices
Mathematical Physics
2009-11-10 v1 Mesoscale and Nanoscale Physics
High Energy Physics - Theory
math.MP
Data Analysis, Statistics and Probability
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.
Cite
@article{arxiv.math-ph/0401038,
title = {Eigenvalue Density of Correlated Complex Random Wishart Matrices},
author = {Steven H. Simon and Aris L. Moustakas},
journal= {arXiv preprint arXiv:math-ph/0401038},
year = {2009}
}