论文标题
弹道lévy步行模型的大偏差
Large deviations of the ballistic Lévy walk model
论文作者
论文摘要
我们研究了弹道lévy步行，这是由于碰撞事件之间无限的平均行进时间。我们的研究重点是从共同起源开始的扩散粒子的密度，该密度受“光”锥$ -V_0 T <x <x <v_0 t $的限制。特别是我们研究了该密度接近“光”锥附近的最大值。扩散密度遵循了莱米特 - 阿尔辛定律，描述了远离“光”锥体的典型波动。然而，这一法律在非物理上的“光”锥层的附近炸开，从某种意义上说，任何有限的时间观察都将永远不会差异。我们声称一个人可以找到两个有关空间密度的法律，第一个是提到的兰克库赛定律，描述了分布的中心部分，第二个是无限密度，说明了大型$ x $的动态。我们确定了一个庞大的位置与描述单一大跳跃原则的最长旅行时间之间的关系。从续签理论中，我们发现该位置的罕见事件的分布与使用速率形式主义的短期“时间”续订数量平均数量有关。
We study the ballistic Lévy walk stemming from an infinite mean traveling time between collision events. Our study focuses on the density of spreading particles all starting from a common origin, which is limited by a `light' cone $-v_0 t<x<v_0 t$. In particular we study this density close to its maximum in the vicinity of the `light' cone. The spreading density follows the Lamperti-arcsine law describing typical fluctuations far from the `light' cone. However this law blows up in the vicinity of the `light' cone horizon which is nonphysical, in the sense that any finite time observation will never diverge. We claim that one can find two laws for the spatial density, the first one is the mentioned Lamperti-arcsine law describing the central part of the distribution and the second is an infinite density illustrating the dynamics for large $x$. We identify the relationship between a large position and the longest traveling time describing the single big jump principle. From the renewal theory we find that the distribution of rare events of the position is related to the derivative of the average of the number of renewals at a short `time' using a rate formalism.
