RT Journal Article
T1 On the robustness of the q-Gaussian family
A1 Sicuro, Gabriele
A1 Tempesta, Piergiulio
A1 Rodriguez, Antonio
A1 Tsallis, Constantino
AB 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.
PB Elsevier Masson
SN 0003-4916
YR 2015
FD 2015-12
LK https://hdl.handle.net/20.500.14352/24299
UL https://hdl.handle.net/20.500.14352/24299
LA eng
NO ©2015 Elsevier Inc.We acknowledge partial support from CNPq and FAPERJ (Brazilian agencies). G. S. and C. T. also acknowledge the financial support of the John Templeton Foundation. The research of P. T. has been supported by the grant FIS2011–22566, Ministerio de Ciencia e Innovación, Spain. A. R. thanks financial support from DGUMEC (Spanish Ministry of Education) through project PHB2007-0095-PC and Comunidad de Madrid through project MODELICO.
NO CNPq (Brazilian agency)
NO FAPERJ (Brazilian agency)
NO John Templeton Foundation
NO Ministerio de Ciencia e Innovacion, Spain
NO DGU-MEC (Spanish Ministry of Education)
NO Comunidad de Madrid
DS Docta Complutense
RD 11 abr 2025