From simplex slicing to sharp reverse H\"older inequalities
Metric Geometry
2026-03-05 v2 Functional Analysis
Probability
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 H\"older-type inequalities.
Cite
@article{arxiv.2505.00944,
title = {From simplex slicing to sharp reverse H\"older inequalities},
author = {James Melbourne and Michael Roysdon and Colin Tang and Tomasz Tkocz},
journal= {arXiv preprint arXiv:2505.00944},
year = {2026}
}
Comments
Final version. To appear in J. Lond. Math. Soc