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 ∈
(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 mathematical 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.
(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 mathematical 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.
| Original language | English |
|---|---|
| Article number | L052101 |
| Number of pages | 5 |
| Journal | Physical Review E |
| Volume | 104 |
| Issue number | 5 |
| Early online date | 8 Nov 2021 |
| DOIs | |
| Publication status | Published - 8 Nov 2021 |
Bibliographical note
ACKNOWLEDGMENTSWe thank J.P. Bouchaud for constructive comments. We acknowledge financial support from the Agence Nationale de la Recherche (ANR grant number ANR-18-
CE45-0012-01) and from the French Research Ministry (MESR) (contract No. 2017-SG-D-09) and from ENS Lyon for SP PhD funding. FJPR acknowledges financial
support from the Carnegie Trust.