Euclidean sections of direct sums of normed spaces

A. E. Litvak*, V. D. Milman

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We study the dimension of "random" Euclidean sections of direct sums of normed spaces. We compare the obtained results with results from [LMS], to show that for the direct sums the standard randomness with respect to the Haar measure on Grassmanian coincides with a much "weaker" randomness of "diagonal" subspaces (Corollary 1.4 and explanation after). We also add some relative information on "phase transition".

Original languageEnglish
Pages (from-to)242-251
Number of pages10
JournalCanadian Mathematical Bulletin
Issue number2
StatePublished - Jun 2003


  • "Random" Euclidean section
  • Dvoretzky theorem
  • Phase transition in asymptotic convexity


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