Hermitian Functional Representation of Free L\'evy Processes
Probability
2020-04-02 v4
Abstract
A functional representation of free L\'evy processes is established via an ensemble of unitarily invariant Hermitian matrix-valued L\'evy processes. This is accomplished by proving functional asymptotics of their empirical spectral processes towards the law of a free L\'evy processes. This result recovers a functional version of Wigner's theorem and introduces a functional version of Marchenko-Pastur's theorem providing the free Poisson process as the noncommutative limit process.
Cite
@article{arxiv.1511.03362,
title = {Hermitian Functional Representation of Free L\'evy Processes},
author = {José-Luis Pérez G. and Víctor Pérez-Abreu and Alfonso Rocha-Arteaga},
journal= {arXiv preprint arXiv:1511.03362},
year = {2020}
}