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Matrix Liberation Process II: Relation to Orbital Free Entropy

Part of: Special matrices Limit theorems Selfadjoint operator algebras

Published online by Cambridge University Press:  28 January 2020

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

Keywords

Random matrixStochastic processUnitary Brownian motionLarge deviationLarge N limitFree probabilityOrbital free entropy

MSC classification

Primary: 60F10: Large deviations
Secondary: 15B52: Random matrices 46L54: Free probability and free operator algebras
Type
Article
Information
Canadian Journal of Mathematics , Volume 73 , Issue 2 , April 2021 , pp. 493 - 541
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Copyright
© 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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