Geodesic
Matrix Liberation Process II: Relation to Orbital Free Entropy
Canadian journal of mathematics, Tome 73 (2021) no. 2, pp. 493-541

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DOI

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.
DOI : 10.4153/S0008414X20000048
Mots-clés : Random matrix, Stochastic process, Unitary Brownian motion, Large deviation, Large N limit, Free probability, Orbital free entropy 
Ueda, Yoshimichi. Matrix Liberation Process II: Relation to Orbital Free Entropy. Canadian journal of mathematics, Tome 73 (2021) no. 2, pp. 493-541. doi: 10.4153/S0008414X20000048
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     author = {Ueda, Yoshimichi},
     title = {Matrix {Liberation} {Process} {II:} {Relation} to {Orbital} {Free} {Entropy}},
     journal = {Canadian journal of mathematics},
     pages = {493--541},
     year = {2021},
     volume = {73},
     number = {2},
     doi = {10.4153/S0008414X20000048},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008414X20000048/}
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