Symmetric $(q,α)$-Stable Distributions. Part II: Second Representation

dc.creatorUmarov, Sabir
dc.creatorTsallis, Constantino
dc.creatorGell-Mann, Murray
dc.creatorSteinberg, Stanly
dc.date2006-06-01
dc.date2008-05-05
dc.date.accessioned2026-07-07T09:36:44Z
dc.date.available2026-07-07T09:36:44Z
dc.descriptionThis paper is a continuation of papers \cite{UmarovTsallisSteinberg,UmarovTsallisGellmannSteinberg}. In Part I \cite{UmarovTsallisGellmannSteinberg} a description (representation) of $(q,α)$-stable distributions based on a $F_q$-transform was given. Here, in Part II, we present another description of these distributions. This approach generalizes results of \cite{UmarovTsallisSteinberg} (which corresponds to $α=2, Q\in [1,3)$) to the whole range of stability and nonextensivity parameters $α\in (0,2]$ and $Q \in [1,3),$ respectively. The present case $α=2$ recovers the $q$-Gaussian distributions. Similar to what is discussed in \cite{UmarovTsallisSteinberg}, a triplet $(q^{\ast},q,q_{\ast})$ arises for which the mapping $F_{q^{\ast}}: \mathcal{G}_{q} \to \mathcal{G}_{q_{\ast}}$ holds. Moreover, by unifying the two preceding descriptions, further possible extensions are discussed and some conjectures are formulated.
dc.description14 pages including 2 figures
dc.identifierhttps://arxiv.org/abs/cond-mat/0606040
dc.identifierhttp://arxiv.org/abs/cond-mat/0606040
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/160221
dc.subjectStatistical Mechanics
dc.subjectProbability
dc.titleSymmetric $(q,α)$-Stable Distributions. Part II: Second Representation
dc.typetext

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