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Power-law and log-normal avalanche size statistics in random growth processes
Stefano Polizzi1,2, Francisco-José Pérez-Reche3, Alain Arneodo2
1Ecole Normale Supérieure de Lyon, 69342 Lyon, France.
Physical Review. E
|December 24, 2021
Summary
This study explores avalanche statistics in random growth models. Key parameters dictate whether avalanche sizes follow stationary, power-law, or log-normal distributions.
Area of Science:
- Statistical Physics
- Complex Systems Modeling
Background:
- Avalanche phenomena are observed across diverse complex systems.
- Understanding the statistical properties of these events is crucial for system analysis.
Purpose of the Study:
- To investigate avalanche statistics in a minimal random growth model.
- To identify the control parameters governing different statistical regimes of avalanche sizes.
Main Methods:
- Utilizing a minimal random growth model with a reproduction rate distribution.
- Performing numerical simulations and statistical analysis.
- Deriving mathematical results to generalize numerical observations.
Main Results:
- Identified three distinct avalanche size regimes: stationary (finite mean/variance), power-law tailed, and non-stationary (log-normal).
- Demonstrated that the mean and variance of the growth rate distribution control the observed regimes.
- Confirmed the existence of these regimes for a broad range of growth rate distributions.
Conclusions:
- The study precisely defines the boundaries between the three avalanche statistics regimes.
- Mathematical insights generalize the findings beyond the specific uniform growth rate distribution used in simulations.
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