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

Shachar Lovett; Sasha Sodin

doi:10.1142/S0219199708002879

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

Shachar Lovett^*
, Sasha Sodin

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

7 Scopus citations

Abstract

It is well known that ^N has subspaces of dimension proportional to N on which the ℓ₁ norm is equivalent to the ℓ₂ norm; however, no explicit constructions are known. Extending an earlier work by Artstein-Avidan and Milman, we prove that such a subspace can be generated using O(N) random bits.

Original language	English
Pages (from-to)	477-489
Number of pages	13
Journal	Communications in Contemporary Mathematics
Volume	10
Issue number	4
DOIs	https://doi.org/10.1142/S0219199708002879
State	Published - Aug 2008
Externally published	Yes

Keywords

Almost Euclidean sections
Cross-polytope
Derandomization
Embedding
K-wise independence

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10.1142/S0219199708002879

Cite this

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abstract = "It is well known that N has subspaces of dimension proportional to N on which the ℓ1 norm is equivalent to the ℓ2 norm; however, no explicit constructions are known. Extending an 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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AB - It is well known that N has subspaces of dimension proportional to N on which the ℓ1 norm is equivalent to the ℓ2 norm; however, no explicit constructions are known. Extending an earlier work by Artstein-Avidan and Milman, we prove that such a subspace can be generated using O(N) random bits.

KW - Almost Euclidean sections

KW - Cross-polytope

KW - Derandomization

KW - Embedding

KW - K-wise independence

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

Abstract

Keywords

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