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

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dc.creatorTsallis, Constantino
dc.creatorQueiros, Silvio M. Duarte
dc.date2007-09-28
dc.date.accessioned2026-07-07T08:49:08Z
dc.date.available2026-07-07T08:49:08Z
dc.descriptionIn 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.
dc.description13 pages, 4 figures. 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
dc.identifierhttps://arxiv.org/abs/0709.4656
dc.identifierhttp://arxiv.org/abs/0709.4656
dc.identifierAIP Conf. Proc. 965, 8 (2007)
dc.identifierdoi:10.1063/1.2828765
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/144193
dc.subjectSoft Condensed Matter
dc.titleNonextensive statistical mechanics and central limit theorems I - Convolution of independent random variables and q-product
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