Logarithmic reduction of the level of randomness in some probabilistic geometric constructions

S. Artstein-Avidan*, V. D. Milman

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

18 Scopus citations

Abstract

Many of the surprising phenomena occurring in high dimensions are proved by use of probabilistic arguments, which show the existence of organized and regular structures but do not hint as to where exactly do these structures lie. It is an intriguing question whether some of them could be realized explicitly. In this paper we show that the amount of randomness used can be reduced significantly in many of these questions from asymptotic convex geometry, and most of the random steps can be substituted by completely explicit algorithmic steps. The main tool we use is random walks on expander graphs.

Original languageEnglish
Pages (from-to)297-329
Number of pages33
JournalJournal of Functional Analysis
Volume235
Issue number1
DOIs
StatePublished - 1 Jun 2006

Funding

FundersFunder number
National Science FoundationDMS-0111298
Bonfils-Stanton Foundation2002-006

    Keywords

    • Asymptotic geometric analysis
    • Explicit constructions
    • Randomness reduction
    • Sections of ℓ

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