Almost Euclidean sections of the N-dimensional cross-polytope using O(N) random bits
Abstract
Description
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. Extending earlier work by Artstein--Avidan and Milman, we prove that such a subspace can be generated using O(N) random bits.
16 pages; minor changes in the introduction to make it more accessible to both Math and CS readers
16 pages; minor changes in the introduction to make it more accessible to both Math and CS readers