Citation

Polizzi S, Pérez-Reche FJ, Arneodo A, Argoul F. Phys. Rev. E 2021; 104(5): L052101.

Copyright

(Copyright © 2021, American Physical Society)

DOI

10.1103/PhysRevE.104.L052101

PMID

34942825

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.

Language: en