Limit laws for boolean convolutions

Details Limit laws for boolean convolutions Limit laws for boolean convolutions

2007-07-23

arxiv.org/abs/0707.3401v2

Mathematics

Operator Algebras

Second version; corrected typos

Scientific paper

We study the distributional behavior for products, and for sums of boolean independent random variables in an infinitesimal triangular array. We show that the limit laws of boolean convolutions are determined by the limit laws of free convolutions, and vice versa. We further use these results to show several connections between the limiting distributional behavior of classical convolutions and that of boolean convolutions. The proof of our results is based on the analytical apparatus developed for free convolutions.

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