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THE NUMBER OF PURE CONVOLUTIONS ARISING FROM CONDITIONALLY FREE CONVOLUTION

Ferenc Oravecz

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Abstract

We show that there are eight special cases of the conditionally free convolution of Bożejko, Leinert and Speicher with the property that in the corresponding moment-cumulant formula no nontrivial weights appear. All the eight convolutions are given. These include the free, the boolean and the Fermi convolutions, another special case of the bold t-free convolution and four more convolution laws that were not treated before.

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What this paper is about

We show that there are eight special cases of the conditionally free convolution of Bożejko, Leinert and Speicher with the property that in the corresponding moment-cumulant formula no nontrivial weights appear. All the eight convolutions are given. These include the free, the boolean and the Fermi convolutions, another special case of the bold t-free convolution and four more convolution laws that were not treated before.

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Available abstract

We show that there are eight special cases of the conditionally free convolution of Bożejko, Leinert and Speicher with the property that in the corresponding moment-cumulant formula no nontrivial weights appear. All the eight convolutions are given. These include the free, the boolean and the Fermi convolutions, another special case of the bold t-free convolution and four more convolution laws that were not treated before.

Key concepts: Convolution (computer science), Convolution power, Convolution theorem, Mathematics, Moment (physics), Cumulant, Property (philosophy), Pure mathematics

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