Note on a q-modified central limit theorem

Abstract

A q-modified version of the central limit theorem due to Umarov et al. affirms that q-Gaussians are attractors under addition and rescaling of certain classes of strongly correlated random variables. The proof of this theorem rests on a nonlinear q-modified Fourier transform. By exhibiting an invariance property we show that this Fourier transform does not have an inverse. As a consequence, the theorem falls short of achieving its stated goal.

10 pages, no figures

References in corpus (4)

• Numerical indications of a q-generalised central limit theorem
• A note on q-Gaussians and non-Gaussians in statistical mechanics
• A generalization of the central limit theorem consistent with nonextensive statistical mechanics
• On a representation of the inverse Fq transform

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