Limit distribution in the $q$-CLT for $q \ge 1$ can not have a compact support
Statistical Mechanics
2010-12-09 v1 Mathematical Physics
math.MP
Abstract
In a recent paper Hilhorst \cite{Hilhorst2010} illustrated that the -Fourier transform for is not invertible in the space of density functions. Using an invariance principle he constructed a family of densities with the same -Fourier transform and claimed that -Gaussians are not mathematically proved to be attractors. We show here that none of the distributions constructed in Hilhorst's counterexamples can be a limit distribution in the -CLT, except the one whose support covers the whole real axis, which is precisely the -Gaussian distribution.
Keywords
Cite
@article{arxiv.1012.1814,
title = {Limit distribution in the $q$-CLT for $q \ge 1$ can not have a compact support},
author = {Sabir Umarov and Constantino Tsallis},
journal= {arXiv preprint arXiv:1012.1814},
year = {2010}
}
Comments
13 pages; no figures