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arXiv · 1902.03873

Analogues of Entropy in Bi-Free Probability Theory: Non-Microstate

Ian Charlesworth·Paul Skoufranis
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Abstract

In this paper, we extend the notion of non-microstate free entropy to the bi-free setting. Using a diagrammatic approach involving bi-non-crossing diagrams, bi-free difference quotients are constructed as analogues of the free partial derivations. Adjoints of bi-free difference quotients are discussed and used to define bi-free conjugate variables. Notions of bi-free Fisher information and non-microstate entropy are defined and properties of free entropy are extended to the bi-free setting.

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BibTeXRIS

Ian Charlesworth, Paul Skoufranis. 2019-02-11. Analogues of Entropy in Bi-Free Probability Theory: Non-Microstate. https://arxiv.org/abs/1902.03873

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