# On nearly radial marginals of high-dimensional probability measures

### Bo'az Klartag

Tel-Aviv University, Israel

## Abstract

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. 723–754

DOI 10.4171/JEMS/213