1 citations · 1 across the 2 of their papers we have counts for
11 papers
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…
Strongly Convex Divergences
James Melbourne
We consider a sub-class of the -divergences satisfying a stronger convexity property, which we refer to as strongly convex, or -convex divergences. We derive new and old rela…
Convex Decreasing Algorithms: Distributed Synthesis and Finite-time Termination in Higher Dimension
James Melbourne, Govind Saraswat, Vivek Khatana +2
We introduce a general mathematical framework for distributed algorithms, and a monotonicity property frequently satisfied in application. These properties are leveraged to provide…
Concentration functions and entropy bounds for discrete log-concave distributions
Sergey G. Bobkov, Arnaud Marsiglietti, James Melbourne
Two-sided bounds are explored for concentration functions and Rényi entropies in the class of discrete log-concave probability distributions. They are used to derive certain varian…
Further investigations of Rényi entropy power inequalities and an entropic characterization of s-concave densities
Jiange Li, Arnaud Marsiglietti, James Melbourne
We investigate the role of convexity in Rényi entropy power inequalities. After proving that a general Rényi entropy power inequality in the style of Bobkov-Chistyakov (2015) fails…