A free logarithmic Sobolev inequality on the circle

Fumio Hiai; Dénes Petz; Yoshimichi Ueda

doi:10.4153/CMB-2006-039-7

A free logarithmic Sobolev inequality on the circle

Fumio Hiai, Dénes Petz, Yoshimichi Ueda

Department of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

4 Citations (Scopus)

Abstract

Free analogues of the logarithmic Sobolev inequality compare the relative free Fisher information with the relative free entropy. In the present paper such an inequality is obtained for measures on the circle. The method is based on a random matrix approximation procedure, and a large deviation result concerning the eigenvalue distribution of special unitary matrices is applied and discussed.

Original language	English
Pages (from-to)	389-406
Number of pages	18
Journal	Canadian Mathematical Bulletin
Volume	49
Issue number	3
DOIs	https://doi.org/10.4153/CMB-2006-039-7
Publication status	Published - Sep 2006

All Science Journal Classification (ASJC) codes

Mathematics(all)

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10.4153/CMB-2006-039-7

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title = "A free logarithmic Sobolev inequality on the circle",

abstract = "Free analogues of the logarithmic Sobolev inequality compare the relative free Fisher information with the relative free entropy. In the present paper such an inequality is obtained for measures on the circle. The method is based on a random matrix approximation procedure, and a large deviation result concerning the eigenvalue distribution of special unitary matrices is applied and discussed.",

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AU - Petz, Dénes

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AB - Free analogues of the logarithmic Sobolev inequality compare the relative free Fisher information with the relative free entropy. In the present paper such an inequality is obtained for measures on the circle. The method is based on a random matrix approximation procedure, and a large deviation result concerning the eigenvalue distribution of special unitary matrices is applied and discussed.

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JO - Canadian Mathematical Bulletin

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A free logarithmic Sobolev inequality on the circle

Abstract

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