# The Abelian distribution

## TL;DR

This paper introduces the Abelian distribution, explores its fundamental properties, and demonstrates its relevance in modeling neural avalanches within fully-connected integrate-and-fire neural systems exhibiting self-organized criticality.

## Contribution

It defines the Abelian distribution and investigates its properties, linking it to neural modeling and avalanche size distributions.

## Key findings

- Abelian distribution models neural avalanche sizes.
- Properties of Abelian distribution are characterized.
- Application to neural systems demonstrates relevance.

## Abstract

We define the Abelian distribution and study its basic properties. Abelian distributions arise in the context of neural modeling and describe the size of neural avalanches in fully-connected integrate-and-fire models of self-organized criticality in neural systems.