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Matrix Liberation Process II: Relation to Orbital Free Entropy

Published online by Cambridge University Press:  28 January 2020

Yoshimichi Ueda
Affiliation:
Graduate School of Mathematics, Nagoya University, Furocho, Chikusaku, Nagoya, 464-8602, Japan Email: ueda@math.nagoya-u.ac.jp
Corresponding
E-mail address:

Abstract

We investigate the concept of orbital free entropy from the viewpoint of the matrix liberation process. We will show that many basic questions around the definition of orbital free entropy are reduced to the question of full large deviation principle for the matrix liberation process. We will also obtain a large deviation upper bound for a certain family of random matrices that is essential to define the orbital free entropy. The resulting rate function is made up into a new approach to free mutual information.

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Article
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© Canadian Mathematical Society 2020

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Footnotes

Supported by Grant-in-Aid for Challenging Exploratory Research 16K13762 and Grant-in-Aid for Scientific Research (B) JP18H01122.

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