An extension of a Bourgain--Lindenstrauss--Milman inequality (2007)
Let || . || be a norm on R^n. Averaging || (\eps_1 x_1, ..., \eps_n x_n) || over all the 2^n choices of \eps = (\eps_1, ..., \eps_n) in {-1, +1}^n, we obtain an expression ||| . ||| which is an...
Bounds on the concentration function in terms of Diophantine approximation (2007)
We demonstrate a simple analytic argument that may be used to bound the Levy concentration function of a sum of independent random variables. The main application is a version of a recent inequality...
Kahane-Khinchin type Averages (2007)
We prove a Kahane-Khinchin type result with a few random vectors, which are distributed independently with respect to an arbitrary log-concave probability measure on $\R^n$. This is an application of...
Polynomial bounds for large Bernoulli sections of $\ell_1^N$ (2006)
Artstein-Avidan, Shiri, Friedland, Omer, Milman, Vitali, Sodin, Sasha
We prove a quantitative version of the bound on the smallest singular value of a Bernoulli covariance matrix (due to Bai and Yin). Then we use this bound, together with several recent developments,...