Scaling of Extreme Events in 2d BTW Sandpile

TL;DR

This paper investigates the statistical properties of extreme avalanches in a 2D Abelian sandpile model, revealing their distributional convergence and scaling behavior, which enhances understanding of extreme events in complex systems.

Contribution

It introduces a novel analysis of extreme event distributions in the sandpile model using GEV distributions and proposes scaling functions that relate activities across different system sizes.

Findings

Largest avalanche size follows Gumbel distribution

Largest avalanche area follows Weibull distribution

Scaling functions enable data collapse across system sizes

Abstract

We study extreme events in a finite-size 2D Abelian sandpile model, specifically focusing on avalanche area and size. Employing the approach of Block Maxima, the study numerically reveals that the rescaled distributions for the largest avalanche size and area converge into the Gumbel and Weibull family of Generalized Extreme Value (GEV) distributions respectively. Numerically, we propose scaling functions for extreme avalanche activities that connect the activities on different length scales. With the help of data collapse, we estimate the precise values of these scaling exponents. The scaling function provides an understanding of the intricate dynamics within the sandpile model, shedding light on the relationship between system size and extreme event characteristics. The findings presented in this paper give valuable insights into the extreme behaviour of the Abelian sandpile model and offer a framework to understand the statistical properties of extreme events in complex systems.