Symmetric $(q,α)$-Stable Distributions. Part I: First Representation

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The classic central limit theorem and $α$-stable distributions play a key role in probability theory, and also in Boltzmann-Gibbs (BG) statistical mechanics. They both concern the paradigmatic case of probabilistic independence of the random variables that are being summed. A generalization of the BG theory, usually referred to as nonextensive statistical mechanics and characterized by the index $q$ ($q=1$ recovers the BG theory), introduces special (long range) correlations between the random variables, and recovers independence for $q=1$. Recently, a $q$-central limit theorem consistent with nonextensive statistical mechanics was established \cite{UmarovTsallisSteinberg} which generalizes the classic Central Limit Theorem. In the present paper we introduce and study symmetric $(q,α)$-stable distributions. The case $q=1$ recovers the Lévy $α$-stable distributions.
17 pages including 3 figures

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Statistical Mechanics, Probability

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http://salesiana.dossiersoluciones.com/handle/123456789/160144

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/cond-mat/0606038
 http://arxiv.org/abs/cond-mat/0606038

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arXiv