Mixed Moments for the Product of Ginibre Matrices
Mathematical Physics
2020-07-21 v1 Statistical Mechanics
High Energy Physics - Theory
math.MP
Machine Learning
Abstract
We study the ensemble of a product of n complex Gaussian i.i.d. matrices. We find this ensemble is Gaussian with a variance matrix which is averaged over a multi-Wishart ensemble. We compute the mixed moments and find that at large , they are given by an enumeration of non-crossing pairings weighted by Fuss-Catalan numbers.
Keywords
Cite
@article{arxiv.2007.10181,
title = {Mixed Moments for the Product of Ginibre Matrices},
author = {Nick Halmagyi and Shailesh Lal},
journal= {arXiv preprint arXiv:2007.10181},
year = {2020}
}
Comments
29 pages