Orbital Free Pressure and Its Legendre Transform

Hiai, Fumio; Ueda, Yoshimichi

doi:10.1007/s00220-014-2135-5

Commun. Math. Phys.

2014

DOI: 10.1007/s00220-014-2135-5

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Orbital Free Pressure and Its Legendre Transform

Fumio Hiai

Yoshimichi Ueda

Abstract: Orbital counterparts of the free pressure and its Legendre transform (or ηentropy) are introduced and studied in comparison with other entropy quantities in free probability theory and in relation to random multi-matrix models.

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2020

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Matrix Liberation Process II: Relation to Orbital Free Entropy

Ueda¹

2020

Can. J. Math.-J. Can. Math.

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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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Matrix Liberation Process II: Relation to Orbital Free Entropy

Ueda¹

2020

Can. J. Math.-J. Can. Math.

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Orbital Free Pressure and Its Legendre Transform

Abstract: Orbital counterparts of the free pressure and its Legendre transform (or ηentropy) are introduced and studied in comparison with other entropy quantities in free probability theory and in relation to random multi-matrix models.

Cited by 1 publication

References 23 publications

Matrix Liberation Process II: Relation to Orbital Free Entropy

Matrix Liberation Process II: Relation to Orbital Free Entropy

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