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arXiv · 0709.4656

Nonextensive statistical mechanics and central limit theorems I - Convolution of independent random variables and q-product

Constantino Tsallis·Silvio M. Duarte Queiros
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Abstract

In this article we review the standard versions of the Central and of the Levy-Gnedenko Limit Theorems, and illustrate their application to the convolution of independent random variables associated with the distribution known as q-Gaussian. This distribution emerges upon extremisation of the nonadditive entropy, basis of nonextensive statistical mechanics. It has a finite variance for q < 5/3, and an infinite one for q > 5/3. We exhibit that, in the case of (standard) independence, the q-Gaussian has either the Gaussian (if q < 5/3) or the a-stable Levy distributions (if q > 5/3) as its attractor in probability space. Moreover, we review a generalisation of the product, the q-product, which plays a central role in the approach of the specially correlated variables emerging within the nonextensive theory.

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Constantino Tsallis, Silvio M. Duarte Queiros. 2007-09-28. Nonextensive statistical mechanics and central limit theorems I - Convolution of independent random variables and q-product. https://doi.org/10.1063/1.2828765

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