A free logarithmic Sobolev inequality on the circle

Fumio Hiai, Dénes Petz, Yoshimichi Ueda

Research output: Contribution to journalArticle

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 languageEnglish
Pages (from-to)389-406
Number of pages18
JournalCanadian Mathematical Bulletin
Volume49
Issue number3
DOIs
Publication statusPublished - Sep 2006

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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