## 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 ∈

(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.

(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 language | English |
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Journal | Physical Review E |

Publication status | Accepted/In press - 14 Oct 2021 |