Nonextensive statistical mechanics and central limit theorems II - Convolution of q-independent random variables
Abstract
In this article we review recent generalisations of the central limit theorem for the sum of specially correlated (or q-independent) variables, focusing on q greater or equal than 1. Specifically, this kind of correlation turns the probability density function known as q-Gaussian, which emerges upon maximisation of the entropy Sq, into an attractor in probability space. Moreover, we also discuss a q-generalisation of a-stable Levy distributions which can as well be stable for this special kind of correlation.Within this context, we verify the emergence of a triplet of entropic indices which relate the form of the attractor, the correlation, and the scaling rate, similar to the q-triplet that connects the entropic indices characterising the sensitivity to initial conditions, the stationary state, and relaxation to the stationary state in anomalous systems.
Cite
@article{arxiv.0709.4661,
title = {Nonextensive statistical mechanics and central limit theorems II - Convolution of q-independent random variables},
author = {Silvio M. Duarte Queiros and Constantino Tsallis},
journal= {arXiv preprint arXiv:0709.4661},
year = {2007}
}
Comments
14 pages, 4 figures, and 1 table. To appear in the Proceedings of the conference CTNEXT07, Complexity, Metastability and Nonextensivity, Catania, Italy, 1-5 July 2007, Eds. S. Abe, H.J. Herrmann, P. Quarati, A. Rapisarda and C. Tsallis (American Institute of Physics, 2008) in press