This work extends simplex slicing to sharp reverse Hölder inequalities in log-concave random variables, indicating a new phase transition.
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.
No takes yet. Share an insight, caveat, or question.
Melbourne et al. (2025) studied this question.
Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context: