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Sicuro, Gabriele and Tempesta, Piergiulio and Rodriguez, Antonio and Tsallis, Constantino (2015) On the robustness of the q-Gaussian family. Annals of physics, 363 . pp. 313-336. ISSN 0003-4916
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Official URL: http://dx.doi.org/10.1016/j.aop.2015.09.006
Abstract
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.
Item Type: | Article |
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Additional Information: | ©2015 Elsevier Inc. |
Uncontrolled Keywords: | Statistical-mechanics; Anomalous diffusion; Tsallis statistics; Phase-space; Entropy; Range |
Subjects: | Sciences > Physics > Physics-Mathematical models Sciences > Physics > Mathematical physics |
ID Code: | 35067 |
Deposited On: | 20 Jan 2016 17:26 |
Last Modified: | 10 Dec 2018 15:09 |
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