On the twisted factorization of the $T$-transform
Operator Algebras
2021-05-21 v1 Probability
Abstract
The amalgamated -transform of a non-commutative distribution was introduced by K.~Dykema. It provides a fundamental tool for computing distributions of random variables in Voiculescu's free probability theory. The -transform factorizes in a rather non-trivial way over a product of free random variables. In this article, we present a simple graphical proof of this property, followed by a more conceptual one, using the abstract setting of an operad with multiplication.
Cite
@article{arxiv.2105.09639,
title = {On the twisted factorization of the $T$-transform},
author = {Kurusch Ebrahimi-Fard and Nicolas Gilliers},
journal= {arXiv preprint arXiv:2105.09639},
year = {2021}
}