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Almost Euclidean sections of the N-dimensional cross-polytope using O(N) random bits

Shachar Lovett·Sasha Sodin
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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.

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Shachar Lovett, Sasha Sodin. 2008-10-20. Almost Euclidean sections of the N-dimensional cross-polytope using O(N) random bits. https://doi.org/10.1142/s0219199708002879

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