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math.FA2007
An extension of a Bourgain--Lindenstrauss--Milman inequality
Omer Friedland, Sasha Sodin
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 ||| . ||…
math.FA2007★ 7 cited
Almost Euclidean sections of the N-dimensional cross-polytope using O(N) random bits
Shachar Lovett, Sasha Sodin
It is well known that R^N has subspaces of dimension proportional to N on which the \ell_1 norm is equivalent to the \ell_2 norm; however, no explicit constructions are known. Exte…
math.FA2006
Polynomial bounds for large Bernoulli sections of
Shiri Artstein-Avidan, Omer Friedland, Vitali Milman +1
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 rec…