Arnaud Marsiglietti
10 papers 143 citations h-index 4 2013–2022
On the entropy power inequality for the R\'enyi entropy of order [0,1]
Using a sharp version of the reverse Young inequality, and a R\'enyi entropy comparison result due to Fradelizi, Madiman, and Wang, the authors are able to derive R\'enyi entropy power...
A lower bound on the differential entropy of log-concave random vectors with applications
We derive a lower bound on the differential entropy of a log-concave random variable $X$ in terms of the $p$-th absolute moment of $X$. The new bound leads to a reverse entropy power inequality...
Variants of the Entropy Power Inequality
An extension of the entropy power inequality to the form $N_r^\alpha(X+Y) \geq N_r^\alpha(X) + N_r^\alpha(Y)$ with arbitrary independent summands $X$ and $Y$ in $\mathbb{R}^n$ is obtained for the...
On the analogue of the concavity of entropy power in the Brunn-Minkowski theory
Elaborating on the similarity between the entropy power inequality and the Brunn-Minkowski inequality, Costa and Cover conjectured in {\it On the similarity of the entropy power inequality and the...
A lower bound on the differential entropy for log-concave random variables with applications to rate-distortion theory
Concentration inequalities for log-concave sequences
We investigate quantitative implications of the notion of log-concavity through a probabilistic interpretation. In particular, we derive concentration inequalities, moment and entropy bounds for...