Entropy and the Discrete Central Limit Theorem

06/01/2021

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by   Lampros Gavalakis, et al.

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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→∞.