A continuous semigroup of notions of independence between the classical and the free oneReport as inadecuate




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1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires 2 CMAP - Centre de Mathématiques Appliquées 3 DMA - Département de Mathématiques et Applications

Abstract : 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.

Keywords : Free Probability Independence Random Matrices Unitary Brownian Motion Convolution Cumulants





Author: Florent Benaych-Georges - Thierry Lévy -

Source: https://hal.archives-ouvertes.fr/



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