From simplex slicing to sharp reverse Hölder inequalities

Abstract

Simplex slicing (Webb, 1996) is a sharp upper bound on the volume of central hyperplane sections of the regular simplex. We extend this to sharp bounds in the probabilistic framework of negative moments, and beyond, of centred log-concave random variables, establishing a curious phase transition of the extremising distribution for new sharp reverse Hölder-type inequalities.

Final version. To appear in J. Lond. Math. Soc