Generalized Central Limit Theorem and Renormalization Group
Mathematical Physics
2016-08-14 v1 Statistical Mechanics
High Energy Physics - Theory
math.MP
Abstract
We introduce a simple instance of the renormalization group transformation in the Banach space of probability densities. By changing the scaling of the renormalized variables we obtain, as fixed points of the transformation, the L\'evy strictly stable laws. We also investigate the behavior of the transformation around these fixed points and the domain of attraction for different values of the scaling parameter. The physical interest of a renormalization group approach to the generalized central limit theorem is discussed.
Cite
@article{arxiv.1009.2899,
title = {Generalized Central Limit Theorem and Renormalization Group},
author = {I. Calvo and J. C. Cuchí and J. G. Esteve and F. Falceto},
journal= {arXiv preprint arXiv:1009.2899},
year = {2016}
}
Comments
16 pages, to appear in J. Stat. Phys