From simplex slicing to sharp reverse Hölder inequalities

2025/05/02 by Melbourne, James, Roysdon, Michael, Tang, Colin +1 · 1 citation
#52A40 (Primary) 52B12 (Secondary) #FOS: Mathematics #Functional Analysis (math.FA) #Metric Geometry (math.MG) #Probability (math.PR)

paper · doi:10.48550/arxiv.2505.00944

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.

Cited by

• Khinchin inequalities for uniforms on spheres with a deficit

Related

• Stability of simplex slicing
• The slicing conjecture via small ball estimates
• Hölder's inequality and its reverse-a probabilistic point of view
• Isoperimetric inequalities in high-dimensional convex sets
• An example related to the slicing inequality for general measures