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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