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 journalArticlepeer-review

5 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 languageEnglish
Pages (from-to)477-489
Number of pages13
JournalCommunications in Contemporary Mathematics
Volume10
Issue number4
DOIs
StatePublished - Aug 2008

Keywords

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

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