Analogues of Entropy in Bi-Free Probability Theory: Non-Microstate
Operator Algebras
2021-06-25 v2 Functional Analysis
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.
Keywords
Cite
@article{arxiv.1902.03873,
title = {Analogues of Entropy in Bi-Free Probability Theory: Non-Microstate},
author = {Ian Charlesworth and Paul Skoufranis},
journal= {arXiv preprint arXiv:1902.03873},
year = {2021}
}
Comments
New version adds a section on non-microstate bi-free entropy dimension