Non-Commutative Functions and Non-Commutative Free Levy-Hincin Formula
Mihai Popa, Victor Vinnikov
TL;DR
This paper extends the theory of infinite divisibility to operator-valued non-commutative probability, providing analogues of the Levy-Hincin formula using advanced mathematical tools.
Contribution
It introduces non-commutative functions and Hilbert bimodule techniques to derive Levy-Hincin type representations for operator-valued free, boolean, and c-free independence.
Findings
Derived Levy-Hincin integral representations in non-commutative settings
Extended infinite divisibility concepts to operator-valued frameworks
Provided new analytical tools for non-commutative probability theory
Abstract
The paper is discussing infinite divisibility in the setting of operator-valued boolean, free and, more general, c-free independences. Particularly, using Hilbert bimodules and non-commutative functions techniques, we obtain analogues of the Levy-Hincin integral representation for infinitely divisible real measures.
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