Note on a q-modified central limit theorem
Statistical Mechanics
2015-05-19 v1 Mathematical Physics
math.MP
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.
Keywords
Cite
@article{arxiv.1008.4259,
title = {Note on a q-modified central limit theorem},
author = {H. J. Hilhorst},
journal= {arXiv preprint arXiv:1008.4259},
year = {2015}
}
Comments
10 pages, no figures