On nearly radial marginals of high-dimensional probability measures

Klartag, Bo'az

doi:10.4171/JEMS/213

Journal of the European Mathematical Society

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Volume 12, Issue 3, 2010, pp. 723–754

DOI: 10.4171/JEMS/213

On nearly radial marginals of high-dimensional probability measures

Bo'az Klartag (1)

(1) School of Mathematical Sciences, Tel-Aviv University, 69978, TEL-AVIV, ISRAEL

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/ε)^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.

Keywords: High-dimensional measures, marginals, Dvoretzky's theorem