论文标题
在中心极限定理的折叠中：莱维步行，较大的偏差和高阶异常扩散
In the folds of the Central Limit Theorem: Lévy walks, large deviations and higher-order anomalous diffusion
论文作者
论文摘要
本文考虑了lévy步行的统计特性，该特性具有随时间的定期正方形位移的常规长期线性缩放，为此，经典中央限制定理的条件适用。尽管有这种特性，但每当过渡时间的统计数据具有幂律尾巴时，它们的高阶力矩都会显示出异常的缩放属性。该现象与经典中央限制定理完全一致，因为它涉及趋向于正态分布的收敛性。与属性密切相关的是，具有有限差异的$ n $独立随机变量的归一化总和的高阶矩可能会偏离无限分布的$ n $倾向于$ n $。通过激发高阶异常扩散的概念，可以彻底分析这些结果的热力学意义。
This article considers the statistical properties of Lévy walks possessing a regular long-term linear scaling of the mean square displacement with time, for which the conditions of the classical Central Limit Theorem apply. Notwithstanding this property, their higher-order moments display anomalous scaling properties, whenever the statistics of the transition times possesses power-law tails. This phenomenon is perfectly consistent with the classical Central Limit Theorem, as it involves the convergence properties towards the normal distribution. It is closely related to the property that the higher order moments of normalized sums of $N$ independent random variables possessing finite variance may deviate, for $N$ tending to infinity, to those of the normal distribution. The thermodynamic implications of these results are thoroughly analyzed by motivating the concept of higher-order anomalous diffusion.
