Work

From simplex slicing to sharp reverse Hölder inequalities

Year: 2026

Type: article

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.

Source: Journal of the London Mathematical Society

DOI: 10.1112/jlms.70461

Authors: James Melbourne, Michael Roysdon, Colin Tang, Tomasz Tkocz

Institutions: Mathematics Research Center, Case Western Reserve University, University of Cincinnati, Carnegie Mellon University

Language: English

Topic: Point processes and geometric inequalities

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,930

Funders: National Science Foundation, University of Crete