English

Central limit theorem, deformed exponentials and superstatistics

Statistical Mechanics 2007-06-04 v1

Abstract

We show that there exists a very natural, superstatistics-linked extension of the central limit theorem (CLT) to deformed exponentials (also called q-Gaussians): This generalization favorably compares with the one provided by S. Umarov and C. Tsallis [arXiv:cond-mat/0703533], since the latter requires a special "q-independence" condition on the data. On the contrary, our CLT proposal applies exactly in the usual conditions in which the classical CLT is used. Moreover, we show that, asymptotically, the q-independence condition is naturally induced by our version of the CLT.

Keywords

Cite

@article{arxiv.0706.0151,
  title  = {Central limit theorem, deformed exponentials and superstatistics},
  author = {C. Vignat and A. Plastino},
  journal= {arXiv preprint arXiv:0706.0151},
  year   = {2007}
}
R2 v1 2026-06-21T08:34:17.437Z