4 papers
The stability of log-supermodularity under convolution
Mokshay Madiman, James Melbourne, Cyril Roberto
We study the behavior of log-supermodular functions under convolution. In particular we show that log-concave product densities preserve log-supermodularity, confirming in the spec…
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.…
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…
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…