Geometry of the Central Limit Theorem in the Nonextensive Case

TL;DR

This paper explores the geometric structure of the Central Limit Theorem when applied to q-Gaussian distributions, using the framework of vectors on a p-sphere to understand their sum behavior.

Contribution

It introduces a geometric perspective on the CLT for q-Gaussians, linking it to the properties of vectors on a p-sphere, which is a novel approach.

Findings

Identifies geometric features underlying the sum of q-Gaussian variables.

Connects the behavior of q-Gaussian sums to uniform distributions on p-spheres.

Provides insights into the structure of nonextensive statistical mechanics.

Abstract

We uncover geometric aspects that underlie the sum of two independent stochastic variables when both are governed by q-Gaussian probability distributions. The pertinent discussion is given in terms of random vectors uniformly distributed on a p-sphere.