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arXiv · 1605.08259

Minimum relative entropy distributions with a large mean are Gaussian

Matteo Smerlak
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Abstract

We consider the following frustrated optimization problem: given a prior probability distribution $q$, find the distribution $p$ minimizing the relative entropy with respect to $q$ such that $\textrm{mean}(p)$ is fixed and large. We show that solutions to this problem are asymptotically Gaussian. As an application we derive an $H$-type theorem for evolutionary dynamics: the entropy of the (standardized) distribution of fitness of a population evolving under natural selection is eventually increasing.

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BibTeXRIS

Matteo Smerlak. 2016-05-26. Minimum relative entropy distributions with a large mean are Gaussian. https://doi.org/10.1103/physreve.94.062107

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