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

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

2007-01-03

arxiv.org/abs/math/0701102v3

Commun. Contemp. Math. 10 (2008), no. 4, 477--489.

Mathematics

Functional Analysis

16 pages; minor changes in the introduction to make it more accessible to both Math and CS readers

Scientific paper

10.1142/S0219199708002879

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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