V-monotone independence
Volume 162 / 2020
Colloquium Mathematicum 162 (2020), 77-107
MSC: Primary 46L53; Secondary 05A18.
DOI: 10.4064/cm7682-4-2019
Published online: 9 April 2020
Abstract
We introduce and study a new notion of non-commutative independence, called V-monotone independence, which can be viewed as an extension of the monotone independence of Muraki. We investigate the combinatorics of mixed moments of V-monotone independent random variables and prove the central limit theorem. We obtain a combinatorial formula for the limit moments and we find the solution of the differential equation for the moment generating function in an implicit form.
