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Entropy and the Discrete Central Limit Theorem (2106.00514v1)
Published 1 Jun 2021 in math.PR, cs.IT, and math.IT
Abstract: 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 $n\to\infty$.