Fluctuations of the Self-Normalized Sum in the Curie-Weiss Model of SOC

TL;DR

This paper extends a key theorem on fluctuations in the Curie-Weiss model of self-organized criticality, providing a concise proof using the Hubbard-Stratonovich transformation and self-normalized sums.

Contribution

It introduces a simplified proof of fluctuation behavior in the Curie-Weiss SOC model leveraging the Hubbard-Stratonovich transformation.

Findings

Extended the main theorem on fluctuations in the Curie-Weiss SOC model

Provided a short, elegant proof using the Hubbard-Stratonovich transformation

Enhanced understanding of self-normalized sums in the model

Abstract

We extend the main theorem of arXiv:1301.6911 about the fluctuations in the Curie-Weiss model of SOC. We present a short proof using the Hubbard-Stratonovich transformation with the self-normalized sum of the random variables.