Note on a q-modified central limit theorem

Details Note on a q-modified central limit theorem Note on a q-modified central limit theorem

2010-08-25

arxiv.org/abs/1008.4259v1

J. Stat. Mech. (2010) P10023

Physics

Condensed Matter

Statistical Mechanics

10 pages, no figures

Scientific paper

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.

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