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

Stefano Polizzi, Francisco Perez-Reche, Alain Arneodo, Françoise Argoul

Research output: Contribution to journalLetterpeer-review


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.
Original languageEnglish
Article numberL052101
Number of pages5
JournalPhysical Review E
Issue number5
Early online date8 Nov 2021
Publication statusPublished - 8 Nov 2021


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