1. CMB 2015 (vol 59 pp. 204)
||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)
||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