On nearly radial marginals of high-dimensional probability measures

TL;DR

This paper demonstrates that high-dimensional probability measures, when projected onto low-dimensional subspaces, tend to exhibit near-spherical symmetry, revealing a universal geometric property.

Contribution

It establishes a general result about the approximate spherical symmetry of low-dimensional marginals of high-dimensional measures, extending previous work in geometric probability.

Findings

Low-dimensional marginals are approximately spherically symmetric.

The result applies to any absolutely continuous probability measure.

This advances understanding of high-dimensional geometric structures.

Abstract

We prove that any absolutely continuous probability measure on a high-dimensional linear space has low-dimensional marginals that are approximately spherically-symmetric.