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Revision #1 to TR07-012 | 20th October 2008 00:00

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

Revision #1
Authors: Shachar Lovett, Sasha Sodin
Accepted on: 20th October 2008 00:00
Keywords:

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.

### Paper:

TR07-012 | 22nd January 2007 00:00

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

TR07-012
Authors: Shachar Lovett, Sasha Sodin
Publication: 5th February 2007 08:47
Keywords:

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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