A law of large numbers for the free multiplicative convolution

Activity: Talks and presentationsTalks and presentations in private or public companies


In classic probability the multiplicative law of large numbers follows from the additive as a corollary. This is not the case in free probability, so although an additive law has been proved in [Lindsay-Pata, 1997] the multiplicative law was only proved recently in [Tucci, 2010] for measures on the positive real line with compact support. In the talk I will present a new proof, which is joint work with Uffe Haagerup, for the multiplicative law. Here we remove the assumption of compact support, using methods very different from Tucci's approach. A special feature of the free multiplicative law is the fact that non degenerate measures will not, as one is used to from classical probability and the free additive law, converge to a Dirac measures. On the contrary the limit uniquely determines the original measure.
Period19. May 2012
Event titleOperator Algebra and Dynamics, NordForsk Network Closing Conference
Event typeConference
LocationGjogv, Faroe Islands