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V-monotone independence

Volume 162 / 2020

Adrian Dacko 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.

Authors

  • Adrian DackoFaculty of Pure and Applied Mathematics
    Wrocław University of Science and Technology
    Wybrzeże Wyspiańskiego 27
    50-370 Wrocław, Poland
    e-mail

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