Article Dans Une Revue Journal of Operator Theory Année : 2021

Nonlinear free Lévy-Khinchine formula and conformal mapping

Résumé

There are two natural notions of Lévy processes in free probability: the first one has free increments with homogeneous distributions and the other has homogeneous transition probabilities [6]. In the two cases one can associate a Nevanlinna function to a free Lévy process. The Nevanlinna functions appearing in the first notion were characterized by Bercovici and Voiculescu [3]. I give an explicit parametrization for the Nevanlinna functions associated with the second kind of free Lévy processes. This gives a nonlinear free Lévy-Khinchine formula.

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hal-02355938 , version 1 (08-11-2019)

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Philippe Biane. Nonlinear free Lévy-Khinchine formula and conformal mapping. Journal of Operator Theory, 2021, 85 (1), pp. 79-99. ⟨10.7900/jot.2019aug02.2267⟩. ⟨hal-02355938⟩
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