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

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 meanā and variance v a. 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 nonstationary 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 they provide a precise definition of the boundaries between the three regimes.
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Contributor : Françoise Argoul Connect in order to contact the contributor
Submitted on : Tuesday, November 9, 2021 - 3:24:44 PM
Last modification on : Tuesday, January 4, 2022 - 6:19:29 AM


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Stefano Polizzi, Francisco-José Pérez-Reche, Alain Arneodo, Françoise Argoul. Power-law and log-normal avalanche size statistics in random growth processes. Physical Review E , American Physical Society (APS), 2021, 104, ⟨10.1103/physreve.104.l052101⟩. ⟨hal-03421092⟩



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