Convolution and Limit Theorems for Conditionally Free Random Variables

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We introduce the notion of a conditionally free product and conditionally free convolution. We describe this convolution both from a combinatorial point of view, by showing its connection with the lattice of non-crossing partitions, and from an analytic point of view, by presenting the basic formula for its $R$-transform. We calculate explicitly the distributions of the conditionally free Gaussian and conditionally free Poisson distribution.
26 pages (pictures from R. Speicher), AMS-TeX 3.0, HD-AM-BLS-01

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Functional Analysis, Operator Algebras

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http://salesiana.dossiersoluciones.com/handle/123456789/152346

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/funct-an/9410004
 http://arxiv.org/abs/funct-an/9410004

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arXiv