### Current browse context:

math.ST

### Change to browse by:

### References & Citations

# Condensed Matter > Statistical Mechanics

# Title: Minimum relative entropy distributions with a large mean are Gaussian

(Submitted on 26 May 2016)

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.

Link back to: arXiv, form interface, contact.