Symmetric $(q,α)$-Stable Distributions. Part II: Second 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 | 2008-05-05 | |
| dc.date.accessioned | 2026-07-07T09:36:44Z | |
| dc.date.available | 2026-07-07T09:36:44Z | |
| dc.description | This 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.description | 14 pages including 2 figures | |
| dc.identifier | https://arxiv.org/abs/cond-mat/0606040 | |
| dc.identifier | http://arxiv.org/abs/cond-mat/0606040 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/160221 | |
| dc.subject | Statistical Mechanics | |
| dc.subject | Probability | |
| dc.title | Symmetric $(q,α)$-Stable Distributions. Part II: Second Representation | |
| dc.type | text |