73 citations · 160 across the 24 of their papers we have counts for
5 papers · 1 filter
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…
Transport-majorization to analytic and geometric inequalities
James Melbourne, Cyril Roberto
We introduce a transport-majorization argument that establishes a majorization in the convex order between two densities, based on control of the gradient of a transportation map b…
Quantitative form of Ball's Cube slicing in and equality cases in the min-entropy power inequality
James Melbourne, Cyril Roberto
We prove a quantitative form of the celebrated Ball's theorem on cube slicing in and obtain, as a consequence, equality cases in the min-entropy power inequality. In…
Concentration Inequalities for Ultra Log-Concave Distributions
Heshan Aravinda, Arnaud Marsiglietti, James Melbourne
We establish concentration inequalities in the class of ultra log-concave distributions. In particular, we show that ultra log-concave distributions satisfy Poisson concentration b…
Bernoulli sums and Rényi entropy inequalities
Mokshay Madiman, James Melbourne, Cyril Roberto
We investigate the Rényi entropy of independent sums of integer valued random variables through Fourier theoretic means, and give sharp comparisons between the variance and the Rén…