A free logarithmic Sobolev inequality on the circle

Fumio Hiai, Dénes Petz, Yoshimichi Ueda

    Research output: Contribution to journalArticlepeer-review

    4 Citations (Scopus)


    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
    Issue number3
    Publication statusPublished - Sept 2006

    All Science Journal Classification (ASJC) codes

    • General Mathematics


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