Central limit theorems for correlated variables: some critical remarks
Abstract
In this talk I first review at an elementary level a selection of central limit theorems, including some lesser known cases, for sums and maxima of uncorrelated and correlated random variables. I recall why several of them appear in physics. Next, I show that there is room for new versions of central limit theorems applicable to specific classes of problems. Finally, I argue that we have insufficient evidence that, as a consequence of such a theorem, q-Gaussians occupy a special place in statistical physics.
Cite
@article{arxiv.0901.1249,
title = {Central limit theorems for correlated variables: some critical remarks},
author = {H. J. Hilhorst},
journal= {arXiv preprint arXiv:0901.1249},
year = {2010}
}
Comments
New paragraph and references added. 20 pages, 9 figures. Text at the basis of a talk presented at the 7th International Conference on Nonextensive Statistical Mechanics: Foundations and Applications (NEXT2008), Foz do Iguacu, Parana, Brazil, 27-31 October 2008