On sharp bounds for marginal densities of product measures Academic Article uri icon

abstract

  • 2016, Hebrew University of Jerusalem. We discuss optimal constants in a recent result of Rudelson and Vershynin on marginal densities. We show that if f is a probability density on Rn of the form f(x) = i=1nfi(xi), where each fi is a density on R, say bounded by one, then the density of any marginal E(f) is bounded by 2k/2, where k is the dimension of E. The proof relies on an adaptation of Balls approach to cube slicing, carried out for functions. Motivated by inequalities for dual affine quermassintegrals, we also prove an isoperimetric inequality for certain averages of the marginals of such f for which the cube is the extremal case.

published proceedings

  • ISRAEL JOURNAL OF MATHEMATICS

author list (cited authors)

  • Livshyts, G., Paouris, G., & Pivovarov, P.

citation count

  • 12

complete list of authors

  • Livshyts, Galyna||Paouris, Grigoris||Pivovarov, Peter

publication date

  • January 2016