BIRS Workshop Lecture Videos

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BIRS Workshop Lecture Videos

Characterization problems in free probability Szpojankowski, Kamil


In classical probability there are known many characterization of probability measures by independence properties. The best example of such result is Bernstein's theorem, which says that for independent X and Y, random variables X+Y and X-Y are independent if and only if X and Y have Gaussian distribution. Surprisingly this theorem and many other characterizations have their counterparts in free probability. My talk will be devoted to present two techniques to deal with characterizations problems in free probability: one combinatorial and one analytic (which uses subordination functions of free additive and multiplicative convolutions). I will also present known analogies between characterization problems in classical and free probability. Talk is based on joint work with Wiktor Ejsmont (Wroclaw) and Uwe Franz (Besancon).

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