On nearly radial marginals of high-dimensional probability measures

Research output: Contribution to journalArticlepeer-review

Abstract

Suppose that μ is an absolutely continuous probability measure on ℝn, for large n. Then μ has low-dimensional marginals that are approximately spherically-symmetric. More precisely, if n ≥ (C/epse;)Cd, then there exist d-dimensional marginals of μ that are ε-far from being spherically- symmetric, in an appropriate sense. Here C > 0 is a universal constant.

Original languageEnglish
Pages (from-to)723-754
Number of pages32
JournalJournal of the European Mathematical Society
Volume12
Issue number3
DOIs
StatePublished - 2010

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