On nearly-radial marginals of high-dimensional probability measures

  • Bo’az Klartag
  • Published 2009
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.