4 papers
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 functiona…
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…
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…
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 obta…