An elementary proof of the inequality for conditional free entropy

  • David Jekel

    Fields Institute for Research in Mathematical Sciences, Toronto, Canada; York University, Toronto, Canada
  • Jennifer Pi

    University of California, Irvine, USA
An elementary proof of the inequality $\chi\leq\chi^{*}$ for conditional free entropy cover
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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.

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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