Almost Euclidean sections of the N-dimensional cross-polytope using O(N) random bits
Abstract
It is well known that RN has subspaces of dimension proportional to N on which the 1 norm is equivalent to the 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.
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