POLIZZI, S.; PEREZ-RECHE, F.-J.; ARNEODO, A.; ARGOUL, F.

doi:10.1103/PhysRevE.104.L052101

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POLIZZI, S.
École normale supérieure de Lyon [ENS de Lyon]
Laboratoire Ondes et Matière d'Aquitaine [LOMA]

PEREZ-RECHE, F.-J.

ARNEODO, A.
Laboratoire Ondes et Matière d'Aquitaine [LOMA]

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Phys.Rev.E. 2021, vol. 104, n° 5, p. L052101

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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 <math><mover accent="true"><mi>a</mi><mo>¯</mo></mover></math> and variance <math><msub><mi>v</mi><mi>a</mi></msub></math>. 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 <math><mrow><mo>∈</mo><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>]</mo></mrow></math>), 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.< Réduire

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

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