Deviations from Gaussianity in deterministic discrete time dynamical systems.

Abstract

In this paper, we examine the deviations from Gaussianity for two types of a random variable converging to a normal distribution, namely, sums of random variables generated by a deterministic discrete time map and a linearly damped variable driven by a deterministic map. We demonstrate how Edgeworth expansions provide a universal description of the deviations from the limiting normal distribution. We derive explicit expressions for these asymptotic expansions and provide numerical evidence of their accuracy.