Symmetric $(q,α)$-Stable Distributions. Part I: First Representation
| dc.creator | Umarov, Sabir | |
| dc.creator | Tsallis, Constantino | |
| dc.creator | Gell-Mann, Murray | |
| dc.creator | Steinberg, Stanly | |
| dc.date | 2006-06-01 | |
| dc.date | 2008-05-03 | |
| dc.date.accessioned | 2026-07-07T09:36:30Z | |
| dc.date.available | 2026-07-07T09:36:30Z | |
| dc.description | 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. | |
| dc.description | 17 pages including 3 figures | |
| dc.identifier | https://arxiv.org/abs/cond-mat/0606038 | |
| dc.identifier | http://arxiv.org/abs/cond-mat/0606038 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/160144 | |
| dc.subject | Statistical Mechanics | |
| dc.subject | Probability | |
| dc.title | Symmetric $(q,α)$-Stable Distributions. Part I: First Representation | |
| dc.type | text |