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