Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8201860 | Annals of Physics | 2015 | 21 Pages |
Abstract
We introduce three deformations, called α-, β- and γ-deformation respectively, of a N-body probabilistic model, first proposed by RodrÃguez et al. (2008), having q-Gaussians as Nââ 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.
Related Topics
Physical Sciences and Engineering
Physics and Astronomy
Physics and Astronomy (General)
Authors
Gabriele Sicuro, Piergiulio Tempesta, Antonio RodrÃguez, Constantino Tsallis,