PIRSA:10070016
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Some limit theorems in operatorvalued noncommutative probability Speaker(s): Serban Belinschi
Abstract: A famous result in classical probability  Hinv{c}in's Theorem  establishes a bijection between infinitely divisible probability distributions and limits of infinitesimal triangular arrays of independent random variables. Analogues of this result have been proved by Bercovici and Pata for scalarvalued {em free probability}. However, very little is known for the case of operatorvalued distributions, when the field of scalars is replaced by a $C^*$algebra; essentially the only result known in full generality that we are aware of is Voiculescu's operatorvalued central limit theorem. In this talk we will use a recent breakthrough in the description of infinite divisibility of operatorvalued distributions achieved by Popa and Vinnikov to prove a Hinv{c}intype theorem for operatorvalued free random variables and to formulate a free  to  conditionally free BercoviciPata bijection. Time permitting, we will discuss in more detail relaations between the operatorvalued free, Boolean and monotone central limits. This is joint work with Mihai V. Popa and Victor Vinnikov.
Date: 05/07/2010  10:30 am
