Hermitian Functional Representation of Free Lévy Processes

José-Luis Pérez G.; Víctor Pérez-Abreu; Alfonso Rocha-Arteaga

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arXiv · 1511.03362

Hermitian Functional Representation of Free Lévy Processes

José-Luis Pérez G.·Víctor Pérez-Abreu·Alfonso Rocha-Arteaga

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Abstract

A functional representation of free Lévy processes is established via an ensemble of unitarily invariant Hermitian matrix-valued Lévy processes. This is accomplished by proving functional asymptotics of their empirical spectral processes towards the law of a free Lévy 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.

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José-Luis Pérez G., Víctor Pérez-Abreu, Alfonso Rocha-Arteaga. 2020-04-01. Hermitian Functional Representation of Free Lévy Processes. https://arxiv.org/abs/1511.03362

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