4 papers · 1 filter
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…