Eigenvalues and Singular Values of Products of Rectangular Gaussian Random Matrices
Statistical Mechanics
2013-05-29 v1 Mathematical Physics
math.MP
Abstract
We derive exact analytic expressions for the distributions of eigenvalues and singular values for the product of an arbitrary number of independent rectangular Gaussian random matrices in the limit of large matrix dimensions. We show that they both have power-law behavior at zero and determine the corresponding powers. We also propose a heuristic form of finite size corrections to these expressions which very well approximates the distributions for matrices of finite dimensions.
Keywords
Cite
@article{arxiv.1007.3594,
title = {Eigenvalues and Singular Values of Products of Rectangular Gaussian Random Matrices},
author = {Z. Burda and A. Jarosz and G. Livan and M. A. Nowak and A. Swiech},
journal= {arXiv preprint arXiv:1007.3594},
year = {2013}
}
Comments
13 pages, 3 figures