On the monotonicity of discrete entropy for log-concave random vectors on ${\mathbb{Z}}^d$

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 $X_1,\dots ,X_{n+1}$ on $\mat…