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}
}