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arXiv · 2105.09639

On the twisted factorization of the $T$-transform

Kurusch Ebrahimi-Fard·Nicolas Gilliers
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Abstract

The amalgamated $T$-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 $T$-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.

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Kurusch Ebrahimi-Fard, Nicolas Gilliers. 2021-05-20. On the twisted factorization of the $T$-transform. https://arxiv.org/abs/2105.09639

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