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)

Access to Document

10.4153/CMB-2006-039-7

Fingerprint Dive into the research topics of 'A free logarithmic Sobolev inequality on the circle'. Together they form a unique fingerprint.

Cite this

@article{66ffe96bcf994b16ae393cc3b6f35a6a,

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.",

author = "Fumio Hiai and D{\'e}nes Petz and Yoshimichi Ueda",

year = "2006",

month = sep,

doi = "10.4153/CMB-2006-039-7",

language = "English",

volume = "49",

pages = "389--406",

journal = "Canadian Mathematical Bulletin",

issn = "0008-4395",

publisher = "Canadian Mathematical Society",

number = "3",

}

TY - JOUR

T1 - A free logarithmic Sobolev inequality on the circle

AU - Hiai, Fumio

AU - Petz, Dénes

AU - Ueda, Yoshimichi

PY - 2006/9

Y1 - 2006/9

N2 - 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.

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.

UR - http://www.scopus.com/inward/record.url?scp=33748927972&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33748927972&partnerID=8YFLogxK

U2 - 10.4153/CMB-2006-039-7

DO - 10.4153/CMB-2006-039-7

M3 - Article

AN - SCOPUS:33748927972

VL - 49

SP - 389

EP - 406

JO - Canadian Mathematical Bulletin

JF - Canadian Mathematical Bulletin

SN - 0008-4395

IS - 3

ER -

A free logarithmic Sobolev inequality on the circle

Abstract

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Cite this