6 papers
Four Function Theorems Through Optimal Transport and Entropic Analogs
Mokshay Madiman, James Melbourne, Cyril Roberto
We study entropic versions of four-function inequalities and give transport proofs of the Euclidean Ahlswede-Daykin theorem and a four-function version of the Prekopa-Leindler ineq…
A Quantitative Entropy Power Inequality for Dependent Random Vectors
Mokshay Madiman, James Melbourne, Cyril Roberto
The entropy power inequality for independent random vectors is a foundational result of information theory, with deep connections to probability and geometric functional analysis.…
Rearrangements and infimum convolutions
Devraj Duggal, James Melbourne, Cyril Roberto
We develop a general comparison result for inf convolution operators related to rearrangement. As a consequence we derive comparison results under spherically symmetric rearrangeme…
Functional Liftings of Restricted Geometric Inequalities
Andreas Malliaris, James Melbourne, Cyril Roberto +1
We investigate what we term "generalized sup-convolutions". We show that functional inequalities that enjoy an interpretation as sup-convolution inequalities can be deduced from th…
Curvature and Other Local Inequalities in Markov Semigroups
Devraj Duggal, Andreas Malliaris, James Melbourne +1
Inspired by the approach of Ivanisvili and Volberg towards functional inequalities for probability measures with strictly convex potentials, we investigate the relationship between…
Minimum entropy of a log-concave variable for fixed variance
James Melbourne, Piotr Nayar, Cyril Roberto
We show that for log-concave real random variables with fixed variance the Shannon differential entropy is minimized for an exponential random variable. We apply this result to der…