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Resumen:
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We introduce three deformations, called ?-, ?-, and ? 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 ?- and ?-deformations are asymptotically scale-invariant, whereas the ?-deformation is not. We prove that, for both ?- and ?-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 ?-case (?- case). In contrast, the ?-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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