Entropy and the Discrete Central Limit Theorem

Lampros Gavalakis, Ioannis Kontoyiannis

Published 2021-06-01Version 1

A strengthened version of the central limit theorem for discrete random variables is established, relying only on information-theoretic tools and elementary arguments. It is shown that the relative entropy between the standardised sum of $n$ independent and identically distributed lattice random variables and an appropriately discretised Gaussian, vanishes as $n\to\infty$.