1. Power-law and log-normal avalanche size statistics in random growth processes
- Author
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Polizzi, S., Perez-Reche, F. -J., Arneodo, A., and Argoul, F.
- Subjects
Physics - Data Analysis, Statistics and Probability ,Condensed Matter - Statistical Mechanics ,Physics - Biological Physics - 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 in (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 analytical 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., Comment: 5 pages, 3 figures
- Published
- 2021
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