Aktiviteter pr. år
Abstract
In classical probability the law of large numbers for the multiplicative convolution follows directly from the law for the additive convolution. In free probability this is not the case. The free additive law was proved by D. Voiculescu in 1986 for probability measures with bounded support and extended to all probability measures with first moment by J.M. Lindsay and V. Pata in 1997, while the free multiplicative law was proved only recently by G. Tucci in 2010. In this paper we extend Tucci’s result to measures with unbounded support while at the same time giving a more elementary proof for the case of bounded support. In contrast to the classical multiplicative convolution case, the limit measure for the free multiplicative law of large numbers is not a Dirac measure, unless the original measure is a Dirac measure. We also show that the mean value of lnx is additive with respect to the free multiplicative convolution while the variance of lnx is not in general additive. Furthermore we study the two parameter family (μα, β)α, β ≥ 0 of measures on (0, ∞) for which the Stransform is given by S μ α,β (z)=(−z) β (1+z) −α , 0 < z < 1.
Originalsprog  Engelsk 

Titel  Operator Algebra and Dynamics : Nordforsk Network Closing Conference, Faroe Islands, May 2012 
Redaktører  Toke M. Carlsen, Søren Eilers, Gunnar Restorff, Sergei Silvestrov 
Forlag  Springer 
Publikationsdato  2013 
Sider  157186 
ISBN (Trykt)  9783642394584 
DOI  
Status  Udgivet  2013 
Navn  Springer Proceedings in Mathematics & Statistics 

Vol/bind  58 
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