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arXiv · 1008.4259

Note on a q-modified central limit theorem

H. J. Hilhorst
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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.

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H. J. Hilhorst. 2010-08-25. Note on a q-modified central limit theorem. https://doi.org/10.1088/1742-5468%2F2010%2F10%2Fp10023

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