An elementary proof of the inequality for conditional free entropy
David Jekel
Fields Institute for Research in Mathematical Sciences, Toronto, Canada; York University, Toronto, CanadaJennifer Pi
University of California, Irvine, USA
Abstract
Through the study of large deviations theory for matrix Brownian motion, Biane, Capitaine, and Guionnet proved the inequality that relates two analogs of entropy in free probability defined by Voiculescu. We give a new proof of that is elementary in the sense that it does not rely on stochastic differential equations and large deviations theory. Moreover, we generalize the result to conditional microstates and non-microstates free entropy.
Cite this article
David Jekel, Jennifer Pi, An elementary proof of the inequality for conditional free entropy. Doc. Math. 29 (2024), no. 5, pp. 1085–1124
DOI 10.4171/DM/969