Power-law and log-normal avalanche size statistics in random growth processes
Abstract
We study the avalanche statistics observed in a minimal random growth model. The growth is governed by a reproduction rate obeying a probability distribution with finite mean a and variance va. These two control parameters determine if the avalanche size tends to a stationary distribution, (Finite Scale statistics with finite mean and variance or Power-Law tailed statistics with exponent in (1, 3]), or instead to a non-stationary regime with Log-Normal statistics. Numerical results and their statistical analysis are presented for a uniformly distributed growth rate, which are corroborated and generalized by analytical results. The latter show that the numerically observed avalanche regimes exist for a wide family of growth rate distributions and provide a precise definition of the boundaries between the three regimes.
Cite
@article{arxiv.2107.08002,
title = {Power-law and log-normal avalanche size statistics in random growth processes},
author = {S. Polizzi and F. -J. Perez-Reche and A. Arneodo and F. Argoul},
journal= {arXiv preprint arXiv:2107.08002},
year = {2021}
}
Comments
5 pages, 3 figures