A theory of singular values for finite free probability
Probability
2023-10-25 v2 Operator Algebras
Abstract
We introduce a finite version of free probability for rectangular matrices that amounts to operations on singular values of polynomials. We show that we can replicate the transforms from free probability, and that asymptotically there is convergence from rectangular finite free probability to rectangular free probability. Lastly, we show that classical distribution results such as a law of large numbers or a central limit theorem can be made explicit in this new framework where random variables are replaced by polynomials.
Cite
@article{arxiv.2208.09768,
title = {A theory of singular values for finite free probability},
author = {Aurelien Gribinski},
journal= {arXiv preprint arXiv:2208.09768},
year = {2023}
}