Nonlinear free Lévy-Khinchine formula and conformal mapping

Philippe Biane

英文摘要：

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. In the two cases one can associate a Nevanlinna function to a free Lévy process. The Nevanlinna functions appearing in the first notion were characterised by Bercovici and Voiculescu. I give an explicit parametrisation 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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