An elementary renormalization-group approach to the Generalized Central Limit Theorem and Extreme Value Distributions
Statistical Mechanics
2020-02-19 v1 Disordered Systems and Neural Networks
Abstract
The Generalized Central Limit Theorem is a remarkable generalization of the Central Limit Theorem, showing that the sum of a large number of independent, identically-distributed (i.i.d) random variables with infinite variance may converge under appropriate scaling to a distribution belonging to a special family known as Levy stable distributions. Similarly, the maximum of i.i.d. variables may converge to a distribution belonging to one of three universality classes (Gumbel, Weibull and Frechet). Here, we rederive these known results following a mathematically non-rigorous yet highly transparent renormalization-group-like approach that captures both of these universal results following a nearly identical procedure.
Cite
@article{arxiv.1908.03580,
title = {An elementary renormalization-group approach to the Generalized Central Limit Theorem and Extreme Value Distributions},
author = {Ariel Amir},
journal= {arXiv preprint arXiv:1908.03580},
year = {2020}
}