| Almost Euclidean sections of the N-dimensional cross-polytope using O(N) random bits (2007) | |||||||||
Abstract | |||||||||
| 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.. Comment: 16 pages; minor changes in the introduction to make it more accessible to both Math and CS readers | |||||||||
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