The normal distribution is ⊞\boxplus-infinitely divisible

We prove that the classical normal distribution is infinitely divisible with respect to the free additive convolution. We study the Voiculescu transform first by giving a survey of its combinatorial implications and then analytically, including a proof of free infinite divisibility. In fact we prove that a subfamily Askey-Wimp-Kerov distributions are freely infinitely divisible, of which the normal distribution is a special case. At the time of this writing this is only the third example known to us of a nontrivial distribution that is infinitely divisible with respect to both classical and free convolution, the others being the Cauchy distribution and the free 1/2-stable distribution.Comment: AMS LaTeX, 29 pages, using tikz and 3 eps figures; new proof including infinite divisibility of certain Askey-Wilson-Kerov distibution

Bornes dans un ensemble ordonné fini‎ : produit contracté, applications

Université : Université scientifique et médicale de Grenobl

Contribution à la théorie des catalogues

Université : Faculté des sciences de l'Université de Grenobl

Le traumatisme dans l'œuvre de Freud et son contexte historique

PARIS7-Bibliothèque centrale (751132105) / SudocSudocFranceF