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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
Downloads: 164
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
Downloads: 159
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.