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Search: MSC category 60E15 ( Inequalities; stochastic orderings )

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1. CMB Online first

Spektor, Susanna
Restricted Khinchine Inequality
We prove a Khintchine type inequality under the assumption that the sum of Rademacher random variables equals zero. We also show a new tail-bound for a hypergeometric random variable.

Keywords:Khintchine inequality, Kahane inequality, Rademacher random variables, hypergeometric distribution.
Categories:46B06, 60E15, 52A23, 46B09

2. CMB 2006 (vol 49 pp. 389)

Hiai, Fumio; Petz, Dénes; Ueda, Yoshimichi
A Free Logarithmic Sobolev Inequality on the Circle
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.

Categories:46L54, 60E15, 94A17

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