Extreme events scaling in self-organized critical models

Abstract 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–Wiesenfeld 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 find ξ > 0. We propose scaling functions for extreme avalanche activities that connect the activities on different length scales. Using the data collapse, we extract the precise value 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.