随机增长过程中的幂律和对数正态雪崩尺寸统计
Power-law and log-normal avalanche size statistics in random growth processes
摘要：
研究了极小随机增长模型中的雪崩统计。增长是由一个服从概率分布的再生产率与有限的平均值a和方差va。这两个控制参数决定了雪崩大小是否倾向于平稳分布（具有有限均值和方差的有限尺度统计量或具有指数的幂律尾统计量（1，3]）），或者相反地倾向于具有对数正态统计量的非平稳状态。给出了均匀增长率情况下的数值结果及其统计分析，并与解析结果进行了验证和推广。后者表明，数值观察到的雪崩制度存在一个广泛的家庭的增长率分布，并提供了一个精确的定义之间的边界的三个制度。
英文摘要：
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 in (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 analytical 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.
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