Partial freeness of random matrices
Probability
2013-05-23 v2 Mathematical Physics
math.MP
Applications
Abstract
We investigate the implications of free probability for random matrices. From rules for calculating all possible joint moments of two free random matrices, we develop a notion of partial freeness which is quantified by the breakdown of these rules. We provide a combinatorial interpretation for partial freeness as the presence of closed paths in Hilbert space defined by particular joint moments. We also discuss how asymptotic moment expansions provide an error term on the density of states. We present MATLAB code for the calculation of moments and free cumulants of arbitrary random matrices.
Cite
@article{arxiv.1204.2257,
title = {Partial freeness of random matrices},
author = {Jiahao Chen and Troy Van Voorhis and Alan Edelman},
journal= {arXiv preprint arXiv:1204.2257},
year = {2013}
}
Comments
8 pages, 2 figures