English

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

R2 v1 2026-06-21T16:04:58.120Z