The randomized dvoretzky’s theorem in ln and the χ-distribution

Konstantin E. Tikhomirov

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


Let ε ∈ (0,1/2). We prove that if for some n > 1 and k > 1, a majority of k-dimensional sections of the ball in ln, is (1 + ε)-spherical then necessarily k ≤ Cε In n/ In where C is a universal constant. The bound for k: is optimal up to the choice of C.

Original languageEnglish (US)
Pages (from-to)455-463
Number of pages9
JournalLecture Notes in Mathematics
StatePublished - 2014

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory


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