%0 Journal Article
%A Sicuro, Gabriele
%A Tempesta, Piergiulio
%A Rodriguez, Antonio
%A Tsallis, Constantino
%T On the robustness of the q-Gaussian family
%D 2015
%@ 0003-4916
%U https://hdl.handle.net/20.500.14352/24299
%X 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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