BIRS Workshop Lecture Videos

Banff International Research Station Logo

BIRS Workshop Lecture Videos

Superconcentration, and randomized Dvoretzky's theorem for spaces with 1-unconditional bases Tikhomirov, Konstantin


Let B be an unconditional convex body in R^n in the ell-position. Then for any small epsilon, and for random subspace E of dimension epsilon*log(n)/log(1/epsilon), distributed according to the rotation-invariant (Haar) measure, the section of B cut by E is (1+C*epsilon)-Euclidean with probability close to one. This shows that the ``worst-case'' dependence on epsilon in the randomized Dvoretzky theorem in the ell-position is significantly better than in John's position.

Item Media

Item Citations and Data


Attribution-NonCommercial-NoDerivatives 4.0 International