Correlation time in extremal self-organized critical models

TL;DR

This paper studies the correlation time in extremal self-organized critical models, revealing power-law scaling and extreme value distribution characteristics through numerical analysis.

Contribution

It introduces a numerical approach to analyze correlation times in extremal SOC models, applying finite-size scaling and extreme value theory to characterize their statistical properties.

Findings

Power-law scaling of mean and variance of correlation time

Data collapse with Gumbel-like extreme value distribution

Correlation time characterized by finite-size scaling laws

Abstract

We investigate correlation time numerically in extremal self-organized critical models, namely, the Bak-Sneppen evolution and the Robin Hood dynamics. The (fitness) correlation time is the duration required for the extinction or mutation of species over the entire spatial region in the critical state. We apply the methods of finite-size scaling and extreme value theory to understand the statistics of the correlation time. We find power-law system size scaling behaviors for the mean, the variance, the mode, and the peak probability of the correlation time. We obtain data collapse for the correlation time cumulative probability distribution, and the scaling function follows the generalized extreme value density close to the Gumbel function.