Probabilistic Operator Algebra Seminar: The Free Nonlinear Levy-Khintchine Formula

Seminar | September 9 | 3-5 p.m. | 736 Evans Hall

 Ian Charlesworth, NSF Postdoctoral Fellow UC Berkeley

 Department of Mathematics

I will speak on recent work of Philippe Biane related to Levy processes in free probability. After recalling the necessary background, I will discuss how free Levy processes with homogeneous transition probabilities are related to Nevanlinna functions which can be explicitly parametrised, and how this gives a nonlinear free Levy-Khintchine formula. Time permitting, I will also explain how these results may be adapted to multiplicative processes on the circle and on the positive real line.