Limit laws for boolean convolutions
Operator Algebras
2007-07-30 v2 Probability
Abstract
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.
Keywords
Cite
@article{arxiv.0707.3401,
title = {Limit laws for boolean convolutions},
author = {Jiun-Chau Wang},
journal= {arXiv preprint arXiv:0707.3401},
year = {2007}
}
Comments
Second version; corrected typos