Conditionally monotone independence and the associated products of graphs
Operator Algebras
2020-04-03 v2 Combinatorics
Probability
Abstract
We reduce the conditionally monotone (c-monotone) independence of Hasebe to tensor independence. For that purpose, we use the approach developed for the reduction of boolean, free and monotone independences to tensor independence. We apply the tensor product realization of c-monotone random variables to introduce the c-comb (loop) product of birooted graphs, a generalization of the comb (loop) product of rooted graphs, and we show that it is related to the c-monotone additive (multiplicative) convolution of distributions.
Keywords
Cite
@article{arxiv.1903.10819,
title = {Conditionally monotone independence and the associated products of graphs},
author = {Romuald Lenczewski},
journal= {arXiv preprint arXiv:1903.10819},
year = {2020}
}
Comments
Corrected proof of Theorem 3.1