On the robustness of the q-Gaussian family
We introduce three deformations, called α-, β-, and γ deformation respectively, of a N-body probabilistic model, first proposed by Rodriguez et al. (2008), having q-Gaussians as N → ∞ limiting probability distributions. The proposed α- and β-deformations are asymptotically scale-invariant, whereas t...
| Autores: | , , , |
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| Formato: | artículo |
| Fecha de publicación: | 2015 |
| País: | España |
| Recursos: | Universidad Complutense de Madrid (UCM) |
| Repositorio: | Docta Complutense |
| Idioma: | inglés |
| OAI Identifier: | oai:docta.ucm.es:20.500.14352/24299 |
| Acesso em linha: | https://hdl.handle.net/20.500.14352/24299 |
| Access Level: | acceso abierto |
| Palavra-chave: | 51-73 Statistical-mechanics Anomalous diffusion Tsallis statistics Phase-space Entropy Range Física-Modelos matemáticos Física matemática |
| Resumo: | We introduce three deformations, called α-, β-, and γ deformation respectively, of a N-body probabilistic model, first proposed by Rodriguez et al. (2008), having q-Gaussians as N → ∞ limiting probability distributions. The proposed α- and β-deformations are asymptotically scale-invariant, whereas the γ-deformation is not. We prove that, for both α- and β-deformations, the resulting deformed triangles still have q-Gaussians as limiting distributions, with a value of q independent (dependent) on the deformation parameter in the α-case (β- case). In contrast, the γ-case, where we have used the celebrated Q-numbers and the Gauss binomial coefficients, yields other limiting probability distribution functions, outside the q-Gaussian family. These results suggest that scale-invariance might play an important role regarding the robustness of the q-Gaussian family. |
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