Entropy and the Discrete Central Limit Theorem

Lampros Gavalakis; Ioannis Kontoyiannis

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arXiv · 2106.00514

Entropy and the Discrete Central Limit Theorem

Lampros Gavalakis·Ioannis Kontoyiannis

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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 $n\to\infty$.

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Lampros Gavalakis, Ioannis Kontoyiannis. 2021-06-01. Entropy and the Discrete Central Limit Theorem. https://arxiv.org/abs/2106.00514

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