Pointwise estimates for marginals of convex bodies

R. Eldan, B. Klartag

Research output: Contribution to journalArticlepeer-review

Abstract

We prove a pointwise version of the multi-dimensional central limit theorem for convex bodies. Namely, let μ be an isotropic, log-concave probability measure on Rn. For a typical subspace E ⊂ Rn of dimension nc, consider the probability density of the projection of μ onto E. We show that the ratio between this probability density and the standard Gaussian density in E is very close to 1 in large parts of E. Here c > 0 is a universal constant. This complements a recent result by the second named author, where the total variation metric between the densities was considered.

Original languageEnglish
Pages (from-to)2275-2293
Number of pages19
JournalJournal of Functional Analysis
Volume254
Issue number8
DOIs
StatePublished - 15 Apr 2008
Externally publishedYes

Keywords

  • Central limit theorem
  • Convex bodies
  • Marginal distribution

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