2 papers
math.MG2026
From simplex slicing to sharp reverse Hölder inequalities
James Melbourne, Michael Roysdon, Colin Tang +1
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 framewo…
math.PR2025
A Rényi entropy interpretation of anti-concentration and noncentral sections of convex bodies
James Melbourne, Tomasz Tkocz, Katarzyna Wyczesany
We extend Bobkov and Chistyakov's (2015) upper bounds on concentration functions of sums of independent random variables to a multivariate entropic setting. The approach is based o…