On the Distribution of an Arbitrary Subset of the Eigenvalues for some Finite Dimensional Random Matrices
Statistics Theory
2020-01-03 v1 Information Theory
math.IT
Statistics Theory
Abstract
We present some new results on the joint distribution of an arbitrary subset of the ordered eigenvalues of complex Wishart, double Wishart, and Gaussian hermitian random matrices of finite dimensions, using a tensor pseudo-determinant operator. Specifically, we derive compact expressions for the joint probability distribution function of the eigenvalues and the expectation of functions of the eigenvalues, including joint moments, for the case of both ordered and unordered eigenvalues.
Keywords
Cite
@article{arxiv.2001.00519,
title = {On the Distribution of an Arbitrary Subset of the Eigenvalues for some Finite Dimensional Random Matrices},
author = {Marco Chiani and Alberto Zanella},
journal= {arXiv preprint arXiv:2001.00519},
year = {2020}
}