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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