Blower, Gordon (2007) *Free and classical entropy over the circle.* Journal of Inequalities in Pure and Applied Mathematics, 8 (1). pp. 1-6. ISSN 1443-5756

## 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.

Item Type: | Article |
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Journal or Publication Title: | Journal of Inequalities in Pure and Applied Mathematics |

Additional Information: | AMS 2000 classification: 60E15; 46L54 |

Uncontrolled Keywords: | Transportation inequality ; free probability ; random matrices |

Subjects: | Q Science > QA Mathematics |

Departments: | Faculty of Science and Technology > Mathematics and Statistics |

ID Code: | 1697 |

Deposited By: | Professor Gordon Blower |

Deposited On: | 18 Feb 2008 09:38 |

Refereed?: | Yes |

Published?: | Published |

Last Modified: | 11 Dec 2016 01:15 |

Identification Number: | |

URI: | http://eprints.lancs.ac.uk/id/eprint/1697 |

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