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Free and classical entropy over the circle.

Research output: Contribution to journalJournal article

Published
<mark>Journal publication date</mark>17/02/2007
<mark>Journal</mark>Journal of Inequalities in Pure and Applied Mathematics
Issue number1
Volume8
Number of pages6
Pages (from-to)1-6
<mark>State</mark>Published
<mark>Original language</mark>English

Abstract

Relative entropy with respect to normalized arclength measure on the circle is greater than or equal to the negative logarithmic energy (Voiculescu's negative free entropy) and is greater than or equal to the modified relative free entropy. This note contains proofs of these inequalities and related consequences of the first Lebedev--Milin inequality.

Bibliographic note

AMS 2000 classification: 60E15; 46L54