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

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

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2 Citations (Scopus)
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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

Bibliographical note

We thank J.P. Bouchaud for constructive comments. We acknowledge financial support from the Agence Nationale de la Recherche (ANR grant number ANR-18-
CE45-0012-01) and from the French Research Ministry (MESR) (contract No. 2017-SG-D-09) and from ENS Lyon for SP PhD funding. FJPR acknowledges financial
support from the Carnegie Trust.


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