2 papers
math.PR2025
On Convex Functions of Gaussian Variables
Maite Fernández-Unzueta, James Melbourne, Gerardo Palafox-Castillo
We investigate a convexity properties for normalized log moment generating function continuing a recent investigation of Chen of convex images of Gaussians. We show that any variab…
cs.IT2021
A discrete complement of Lyapunov's inequality and its information theoretic consequences
James Melbourne, Gerardo Palafox-Castillo
We establish a reversal of Lyapunov's inequality for monotone log-concave sequences, settling a conjecture of Havrilla-Tkocz and Melbourne-Tkocz. A strengthened version of the same…