Research output: Contribution to Journal/Magazine › Journal article › peer-review

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In: Journal of Inequalities in Pure and Applied Mathematics, Vol. 8, No. 1, 17.02.2007, p. 1-6.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Blower, G 2007, 'Free and classical entropy over the circle.', *Journal of Inequalities in Pure and Applied Mathematics*, vol. 8, no. 1, pp. 1-6. <http://jipam.vu.edu.au/article.php?sid=814>

Blower, G. (2007). Free and classical entropy over the circle. *Journal of Inequalities in Pure and Applied Mathematics*, *8*(1), 1-6. http://jipam.vu.edu.au/article.php?sid=814

Blower G. Free and classical entropy over the circle. Journal of Inequalities in Pure and Applied Mathematics. 2007 Feb 17;8(1):1-6.

@article{d60e458659234c10a7ce47152392eb22,

title = "Free and classical entropy over the circle.",

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.",

keywords = "Transportation inequality, free probability, random matrices",

author = "Gordon Blower",

note = "AMS 2000 classification: 60E15; 46L54",

year = "2007",

month = feb,

day = "17",

language = "English",

volume = "8",

pages = "1--6",

journal = "Journal of Inequalities in Pure and Applied Mathematics",

issn = "1443-5756",

publisher = "Victoria University of Technology",

number = "1",

}

TY - JOUR

T1 - Free and classical entropy over the circle.

AU - Blower, Gordon

N1 - AMS 2000 classification: 60E15; 46L54

PY - 2007/2/17

Y1 - 2007/2/17

N2 - 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.

AB - 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.

KW - Transportation inequality

KW - free probability

KW - random matrices

M3 - Journal article

VL - 8

SP - 1

EP - 6

JO - Journal of Inequalities in Pure and Applied Mathematics

JF - Journal of Inequalities in Pure and Applied Mathematics

SN - 1443-5756

IS - 1

ER -