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Journal of the European Mathematical Society

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Volume 12, Issue 3, 2010, pp. 723–754
DOI: 10.4171/JEMS/213

Published online: 2010-04-20

On nearly radial marginals of high-dimensional probability measures

Bo'az Klartag[1]

(1) Tel-Aviv University, 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

Klartag Bo'az: On nearly radial marginals of high-dimensional probability measures. J. Eur. Math. Soc. 12 (2010), 723-754. doi: 10.4171/JEMS/213