A continuous semigroup of notions of independence between the classical and the free one

Details A continuous semigroup of notions of independence between the classical and the free one A continuous semigroup of notions of independence between the classical and the free one

2008-11-14

arxiv.org/abs/0811.2335v2

Mathematics

Probability

27 pages

Scientific paper

In this paper, we investigate a continuous family of notions of independence which interpolates between the classical and free ones for non-commutative random variables. These notions are related to the liberation process introduced by D. Voiculescu. To each notion of independence correspond new convolutions of probability measures, for which we establish formulae and of which we compute simple examples. We prove that there exists no reasonable analogue of classical and free cumulants associated to these notions of independence.

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