@article{ref1,
title="Power-law and log-normal avalanche size statistics in random growth processes",
journal="Physical review. E",
year="2021",
author="Polizzi, Stefano and Pérez-Reche, Francisco-José and Arneodo, Alain and Argoul, Françoise",
volume="104",
number="5",
pages="L052101-L052101",
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[over ¯] and variance v_{a}. 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 ∈(1,3]), or instead to a nonstationary 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 mathematical results. The latter show that the numerically observed avalanche regimes exist for a wide family of growth rate distributions, and they provide a precise definition of the boundaries between the three regimes.<p /> <p>Language: en</p>",
language="en",
issn="2470-0045",
doi="10.1103/PhysRevE.104.L052101",
url="http://dx.doi.org/10.1103/PhysRevE.104.L052101"
}