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Convolution and Limit Theorems for Conditionally Free Random Variables

Marek Bozejko·Michael Leinert·Roland Speicher
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Abstract

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.

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BibTeXRIS

Marek Bozejko, Michael Leinert, Roland Speicher. 1994-10-17. Convolution and Limit Theorems for Conditionally Free Random Variables. https://arxiv.org/abs/funct-an/9410004

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