42 citations · 79 across the 18 of their papers we have counts for
25 papers
Majorization, Entropy and Concentration Inequalities for Discrete -Concave Random Variables
Abdulmajeed Alqasem, Heshan Aravinda, Arnaud Marsiglietti
We establish a maximum-variance inequality for discrete -concave random variables in the regime , extending corresponding results beyond the discrete log-concave setti…
A note on the Littlewood-Offord problem for discrete log-concave distributions
Arnaud Marsiglietti, James Melbourne
We present an extension of the famous Littlewood-Offord problem when Bernoulli distributions are replaced with discrete log-concave distributions. A variant of the Littlewood-Offor…
On a Conjecture of Feige for Discrete Log-Concave Distributions
Abdulmajeed Alqasem, Heshan Aravinda, Arnaud Marsiglietti +1
A remarkable conjecture of Feige (2006) asserts that for any collection of independent non-negative random variables , each with expectation at most ,…
Concentration inequalities for log-concave sequences
Arnaud Marsiglietti, James Melbourne
We investigate quantitative implications of the notion of log-concavity through a probabilistic interpretation. In particular, we derive concentration inequalities, moment and entr…
On the Equivalence of Statistical Distances for Isotropic Convex Measures
Arnaud Marsiglietti, Puja Pandey
We establish quantitative comparisons between classical distances for probability distributions belonging to the class of convex probability measures. Distances include total varia…
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…
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…
Geometric and Functional Inequalities for Log-concave Probability Sequences
Arnaud Marsiglietti, James Melbourne
We investigate geometric and functional inequalities for the class of log-concave probability sequences. We prove dilation inequalities for log-concave probability measures on the…
Entropic CLT for smoothed convolutions and associated entropy bounds
Sergey G. Bobkov, Arnaud Marsiglietti
We explore an asymptotic behavior of entropies for sums of independent random variables that are convolved with a small continuous noise.
Local limit theorems for smoothed Bernoulli and other convolutions
Sergey G. Bobkov, Arnaud Marsiglietti
We explore an asymptotic behavior of densities of sums of independent random variables that are convoluted with a small continuous noise.
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…
Asymptotic behavior of Rényi entropy in the central limit theorem
Sergey G. Bobkov, Arnaud Marsiglietti
We explore an asymptotic behavior of Rényi entropy along convolutions in the central limit theorem with respect to the increasing number of i.i.d. summands. In particular, the prob…
On the entropy power inequality for the Rényi entropy of order [0,1]
Arnaud Marsiglietti, James Melbourne
Using a sharp version of the reverse Young inequality, and a Rényi entropy comparison result due to Fradelizi, Madiman, and Wang, the authors are able to derive Rényi entropy power…
A lower bound on the differential entropy of log-concave random vectors with applications
Arnaud Marsiglietti, Victoria Kostina
We derive a lower bound on the differential entropy of a log-concave random variable in terms of the -th absolute moment of . The new bound leads to a reverse entropy pow…
The convexification effect of Minkowski summation
Matthieu Fradelizi, Mokshay Madiman, Arnaud Marsiglietti +1
Let us define for a compact set the sequence $$ A(k) = \left\{\frac{a_1+\cdots +a_k}{k}: a_1, \ldots, a_k\in A\right\}=\frac{1}{k}\Big(\underset{k\ {\rm ti…
Variants of the Entropy Power Inequality
Sergey Bobkov, Arnaud Marsiglietti
An extension of the entropy power inequality to the form with arbitrary independent summands and in is obtained for the…
On the stability of Brunn-Minkowski type inequalities
Andrea Colesanti, Galyna V. Livshyts, Arnaud Marsiglietti
Log-Brunn-Minkowski inequality was conjectured by Boröczky, Lutwak, Yang and Zhang \cite{BLYZ}, and it states that a certain strengthening of the classical Brunn-Minkowski inequali…
Do Minkowski averages get progressively more convex?
Matthieu Fradelizi, Mokshay Madiman, Arnaud Marsiglietti +1
Let us define, for a compact set , the Minkowski averages of : $$ A(k) = \left\{\frac{a_1+\cdots +a_k}{k} : a_1, \ldots, a_k\in A\right\}=\frac{1}{k}\Big…
Borell's generalized Prékopa-Leindler inequality: A simple proof
Arnaud Marsiglietti
We present a simple proof of Christer Borell's general inequality in the Brunn-Minkowski theory. We then discuss applications of Borell's inequality to the log-Brunn-Minkowski ineq…
A note on the convex infimum convolution inequality
Naomi Feldheim, Arnaud Marsiglietti, Piotr Nayar +1
We characterize the symmetric measures which satisfy the one dimensional convex infimum convolution inequality of Maurey. For these measures the tensorization argument yields the t…
On the Brunn-Minkowski inequality for general measures with applications to new isoperimetric-type inequalities
Galyna Livshyts, Arnaud Marsiglietti, Piotr Nayar +1
In this paper we present new versions of the classical Brunn-Minkowski inequality for different classes of measures and sets. We show that the inequality \[ μ(λA + (1-λ)B)^{1/n} \g…
A note on an -Brunn-Minkowski inequality for convex measures in the unconditional case
Arnaud Marsiglietti
We consider a different -Minkowski combination of compact sets in than the one introduced by Firey and we prove an -Brunn-Minkowski inequality, $p \in [0,1…
On the improvement of concavity of convex measures
Arnaud Marsiglietti
We prove that a general class of measures, which includes -concave measures, is -concave according to the terminology of Borell, with additional assumptions on t…
Concavity properties of extensions of the parallel volume
Arnaud Marsiglietti
In this paper we establish concavity properties of two extensions of the classical notion of the outer parallel volume. On the one hand, we replace the Lebesgue measure by more gen…