Almost Euclidean sections in symmetric spaces and concentration of order statistics

Konstantin E. Tikhomirov

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

We prove that for any symmetric n-dimensional normed space E and any ε. >. 0, E contains a (1. +. ε)-Euclidean subspace of dimension at least cln. n/ln(1/ε), where c is an absolute constant. The proof is based on a concentration property of order statistics of random vectors with i.i.d. coordinates.

Original languageEnglish (US)
Pages (from-to)2074-2088
Number of pages15
JournalJournal of Functional Analysis
Volume265
Issue number9
DOIs
StatePublished - Nov 1 2013

All Science Journal Classification (ASJC) codes

  • Analysis

Keywords

  • Dvoretzky's theorem
  • Order statistic
  • Symmetric basis

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