4 papers
The M-ellipsoid, Symplectic Capacities and Volume
Shiri Artstein-Avidan, Vitali D. Milman, Yaron Ostrover
In this work we bring together tools and ideology from two different fields, Symplectic Geometry and Asymptotic Geometric Analysis, to arrive at some new results. Our main result i…
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…
On convexified packing and entropy duality
S. Artstein, V. Milman, S. J. Szarek +1
A 1972 duality conjecture due to Pietsch asserts that the entropy numbers of a compact operator acting between two Banach spaces and those of its adjoint are (in an appropriate sen…
Duality of metric entropy
S. Artstein, V. Milman, S. J. Szarek
For two convex bodies K and T in , the covering number of K by T, denoted N(K,T), is defined as the minimal number of translates of T needed to cover K. Let us denote by …