Suppose that μ_ is an absolutely continuous probability measure on ℝ_n, 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.
Cite this article
Bo'az Klartag, On nearly radial marginals of high-dimensional probability measures. J. Eur. Math. Soc. 12 (2010), no. 3, pp. 723–754DOI 10.4171/JEMS/213