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arXiv · 2107.08002

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

S. Polizzi·F. -J. Perez-Reche·A. Arneodo·F. Argoul
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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.

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S. Polizzi, F. -J. Perez-Reche, A. Arneodo, F. Argoul. 2021-07-16. Power-law and log-normal avalanche size statistics in random growth processes. https://doi.org/10.1103/physreve.104.l052101

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