随机加速步行者的人类流动随机模型
A stochastic model of randomly accelerated walkers for human mobility
摘要：
近年来，大型数据库的出现使得人们可以研究许多复杂系统的宏观性质。然而，在没有任何动态知识的情况下，从经验数据拟合中推断模型可能会导致错误的解释[6]。我们在人类流动[1-3]和觅食人类模式[4]的情况下说明了这一点，其中跳跃大小的经验长尾分布与称为Lévy flights [5]的无标度超扩散随机游动相关联。在这里，我们引入了一类新的加速随机游动，其中速度由于随机时间的加速度变化而变化，结合旅行时间的峰值分布[7]，显示了一个跳跃长度分布，很容易被误解为截断幂律，但不受大波动的影响。这个随机模型使我们能够解释关于意大利78万辆私家车运动的经验观察，更普遍地说，可以更深入地定量了解人类流动。
英文摘要：
The recent availability of large databases allows to study macroscopic properties of many complex systems. However, inferring a model from a fit of empirical data without any knowledge of the dynamics might lead to erroneous interpretations [6]. We illustrate this in the case of human mobility [1-3] and foraging human patterns [4] where empirical long-tailed distributions of jump sizes have been associated to scale-free super-diffusive random walks called Lévy flights [5]. Here, we introduce a new class of accelerated random walks where the velocity changes due to acceleration kicks at random times, which combined with a peaked distribution of travel times [7], displays a jump length distribution that could easily be misinterpreted as a truncated power law, but that is not governed by large fluctuations. This stochastic model allows us to explain empirical observations about the movements of 780,000 private vehicles in Italy, and more generally, to get a deeper quantitative understanding of human mobility.
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