154 citations · 1.3k across the 48 of their papers we have counts for
8 papers · 1 filter
Integral inequalities for -convolutions of -concave functions
Mokshay Madiman, Auttawich Manui, Bartłomiej Zawalski +1
Classical sumset inequalities originating in additive combinatorics admit geometric analogues for convex bodies in finite-dimensional real vector spaces, as recently developed by F…
Weighted Brunn-Minkowski Theory II: Inequalities for Mixed Measures and Applications
Matthieu Fradelizi, Dylan Langharst, Mokshay Madiman +1
In "Weighted Brunn-Minkowski Theory I", the prequel to this work, we discussed how recent developments on concavity of measures have laid the foundations of a nascent weighted Brun…
An Exact Upper Bound on the Lebesgue Constant and The -Rényi Entropy Power Inequality for Integer Valued Random Variables
Peng Xu, Mokshay Madiman, James Melbourne
In this paper, we proved an exact asymptotically sharp upper bound of the Lebesgue Constant (i.e. the norm of Dirichlet kernel) for . As an application, we also…
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…
On the problem of reversibility of the entropy power inequality
Sergey G. Bobkov, Mokshay M. Madiman
As was shown recently by the authors, the entropy power inequality can be reversed for independent summands with sufficiently concave densities, when the distributions of the summa…
Reverse Brunn-Minkowski and reverse entropy power inequalities for convex measures
Sergey Bobkov, Mokshay Madiman
We develop a reverse entropy power inequality for convex measures, which may be seen as an affine-geometric inverse of the entropy power inequality of Shannon and Stam. The special…