Extreme events scaling in self-organized critical models

Fuente: arXiv
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Main Authors: Quadir, Abdul, Jafri, Haider Hasan
Format: Preprint
Published: 2025
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author Quadir, Abdul
Jafri, Haider Hasan
author_facet Quadir, Abdul
Jafri, Haider Hasan
contents We study extreme events of avalanche activities in finite-size two-dimensional self-organized critical (SOC) models, specifically the stochastic Manna model (SMM) and the Bak-Tang-Weisenfeld (BTW) sandpile model. Employing the approach of block maxima, the study numerically reveals that the distributions for extreme avalanche size and area follow the generalized extreme value (GEV) distribution. The extreme avalanche size follows the Gumbel distribution with shape parameter $ξ=0$ while in the case of the extreme avalanche area, we report $ξ>0$. 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 critical exponents. The scaling functions provide an understanding of the intricate dynamics for different variants of the sandpile model, shedding light on the relationship between system size and extreme event characteristics. Our findings give insight into the extreme behavior of SOC models and offer a framework to understand the statistical properties of extreme events.
format Preprint
id arxiv_https___arxiv_org_abs_2510_08733
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Extreme events scaling in self-organized critical models
Quadir, Abdul
Jafri, Haider Hasan
Statistical Mechanics
We study extreme events of avalanche activities in finite-size two-dimensional self-organized critical (SOC) models, specifically the stochastic Manna model (SMM) and the Bak-Tang-Weisenfeld (BTW) sandpile model. Employing the approach of block maxima, the study numerically reveals that the distributions for extreme avalanche size and area follow the generalized extreme value (GEV) distribution. The extreme avalanche size follows the Gumbel distribution with shape parameter $ξ=0$ while in the case of the extreme avalanche area, we report $ξ>0$. 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 critical exponents. The scaling functions provide an understanding of the intricate dynamics for different variants of the sandpile model, shedding light on the relationship between system size and extreme event characteristics. Our findings give insight into the extreme behavior of SOC models and offer a framework to understand the statistical properties of extreme events.
title Extreme events scaling in self-organized critical models
topic Statistical Mechanics
url https://arxiv.org/abs/2510.08733