Power-law and log-normal avalanche size statistics in random growth processes

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...

Full description

Saved in:
Bibliographic Details
Published in:Physical review. E 2021-11, Vol.104 (5), p.L052101-L052101, Article Paper No. L052101, 5
Main Authors: Polizzi, Stefano, Pérez-Reche, Francisco-José, Arneodo, Alain, Argoul, Françoise
Format: Article
Language:English
Subjects:
Adaptation and Self-Organizing Systems
Biological Physics
Condensed Matter
Nonlinear Sciences
Physics
Statistical Mechanics
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:2470-0045
2470-0053
DOI:10.1103/physreve.104.l052101