Almost Euclidean sections of the N-dimensional cross-polytope using O(N) random bits
Functional Analysis
2009-04-12 v3 Computational Complexity
Metric Geometry
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.
Keywords
Cite
@article{arxiv.math/0701102,
title = {Almost Euclidean sections of the N-dimensional cross-polytope using O(N) random bits},
author = {Shachar Lovett and Sasha Sodin},
journal= {arXiv preprint arXiv:math/0701102},
year = {2009}
}
Comments
16 pages; minor changes in the introduction to make it more accessible to both Math and CS readers