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

Stefano Polizzi (1, 2) , Francisco-José Pérez-Reche (3) , Alain Arneodo (1) , Françoise Argoul (1, 2)

1 LOMA - Laboratoire Ondes et Matière d'Aquitaine
2 Phys-ENS - Laboratoire de Physique de l'ENS Lyon
3 University of Aberdeen

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 meanā 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.

Domaines: Biophysique [physics.bio-ph]; Adaptation et Systèmes auto-organisés [nlin.AO]; Mécanique statistique [cond-mat.stat-mech]

Stefano Polizzi, Francisco-José Pérez-Reche, Alain Arneodo, Françoise Argoul. Power-law and log-normal avalanche size statistics in random growth processes. Physical Review E , 2021, 104, ⟨10.1103/physreve.104.l052101⟩. ⟨hal-03421092⟩