5 papers · 1 filter
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…
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…
Conditions for equality and stability in Shannon's and Tao's entropy power inequalities
Lampros Gavalakis, Ioannis Kontoyiannis
We show that there is equality in Shannon's Entropy Power Inequality (EPI) if and only if the random variables involved are Gaussian, assuming nothing beyond the existence of diffe…
Finite de Finetti bounds in relative entropy
Lampros Gavalakis, Oliver Johnson, Ioannis Kontoyiannis
We review old and recent finite de Finetti theorems in total variation distance and in relative entropy, and we highlight their connections with bounds on the difference between sa…
Relative entropy bounds for sampling with and without replacement
Oliver Johnson, Lampros Gavalakis, Ioannis Kontoyiannis
Sharp, nonasymptotic bounds are obtained for the relative entropy between the distributions of sampling with and without replacement from an urn with balls of colors. Our…