On the role of ergodicity and mixing in the central limit theorem for Casati-Prosen triangle map variables

Details On the role of ergodicity and mixing in the central limit theorem for Casati-Prosen triangle map variables On the role of ergodicity and mixing in the central limit theorem for Casati-Prosen triangle map variables

2008-02-04

arxiv.org/abs/0802.0406v4

Phys. Lett. A 373, 1514-1518 (2009)

Physics

Condensed Matter

Statistical Mechanics

14 pages. To appear in Physics Letters A

Scientific paper

10.1016/j.physleta.2009.02.055

In this manuscript we analyse the behaviour of the probability density function of the sum of $N$ deterministic variables generated from the triangle map of Casati-Prosen. For the case in which the map is both ergodic and mixing the resulting probability density function quickly concurs with the Normal distribution. When these properties are modified the resulting probability density functions are described by power-laws. Moreover, contrarily to what it would be expected, as the number of added variables $N$ increases the distance to Gaussian distribution increases. This behaviour goes against standard central limit theorem. By extrapolation of our finite size results we preview that in the limit of $N$ going to infinity the distribution has the same asymptotic decay as a Lorenztian (or a $q=2$-Gaussian).

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