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math.OA2019★ 2 cited
Analogues of Entropy in Bi-Free Probability Theory: Microstates
Ian Charlesworth, Paul Skoufranis
In this paper, we extend the notion of microstate free entropy to the bi-free setting. In particular, using the bi-free analogue of random matrices, microstate bi-free entropy is d…
math.OA2019
Analogues of Entropy in Bi-Free Probability Theory: Non-Microstate
Ian Charlesworth, Paul Skoufranis
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 quot…