6 papers
Hermite-Fisher bounds and stability for min-entropy power inequalities
Silouanos Brazitikos, Martin Rapaport, Tomasz Tkocz
We derive explicit lower bounds for relative Fisher information by combining a variational principle with suitably orthogonalized Hermite-polynomial test functions. The resulting c…
Entropic analogues of Grünbaum's inequality
Matthieu Fradelizi, Lampros Gavalakis, Martin Rapaport
The classical Grünbaum inequality asserts that the proportion of the volume of a convex body cut off by a halfspace containing its barycenter is at least . From its functional…
Negative Moments of Steinhaus Sums
Martin Rapaport, Tomasz Tkocz, Isabella Wu
We prove a sharp upper bound on negative moments of sums of independent Steinhaus random variables (that is uniform on circles in the plane). Together with the series of earlier wo…
Entropic versions of Bergström's and Bonnesen's inequalities
Matthieu Fradelizi, Lampros Gavalakis, Martin Rapaport
We establish analogues of the Bergström and Bonnesen inequalities, related to determinants and volumes respectively, for the entropy power and for the Fisher information. The obtai…
On the monotonicity of discrete entropy for log-concave random vectors on
Matthieu Fradelizi, Lampros Gavalakis, Martin Rapaport
We prove the following type of discrete entropy monotonicity for sums of isotropic, log-concave, independent and identically distributed random vectors on $\mat…
Criteria for entropic curvature on graph spaces
Martin Rapaport, Paul-Marie Samson
In this paper we establish new simple local geometric criteria for discrete entropic curvature introduced in [47] that are powerful enough to capture many geometric properties of c…