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Revision #1 to TR07-012 | 20th October 2008 00:00
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#### Almost Euclidean sections of the N-dimensional cross-polytope using O(N) random bits

**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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TR07-012 | 22nd January 2007 00:00
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#### Almost Euclidean sections of the N-dimensional cross-polytope using O(N) random bits

**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.