Régnier Léo, Dolgushev Maxim, Redner S, Bénichou Olivier
Laboratoire de Physique Théorique de la Matière Condensée, CNRS/Sorbonne University, 4 Place Jussieu, 75005 Paris, France.
Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, New Mexico 87501 USA.
Phys Rev E. 2022 Jun;105(6-1):064104. doi: 10.1103/PhysRevE.105.064104.
We develop a framework to determine the complete statistical behavior of a fundamental quantity in the theory of random walks, namely, the probability that n_{1},n_{2},n_{3},... distinct sites are visited at times t_{1},t_{2},t_{3},.... From this multiple-time distribution, we show that the visitation statistics of one-dimensional random walks are temporally correlated, and we quantify the non-Markovian nature of the process. We exploit these ideas to derive unexpected results for the two-time trapping problem and to determine the visitation statistics of two important stochastic processes, the run-and-tumble particle and the biased random walk.
我们开发了一个框架，以确定随机游走理论中一个基本量的完整统计行为，即，在时刻(t_{1},t_{2},t_{3},...)访问(n_{1},n_{2},n_{3},...)个不同位点的概率。从这个多次分布中，我们表明一维随机游走的访问统计在时间上是相关的，并且我们量化了该过程的非马尔可夫性质。我们利用这些想法推导出关于两次捕获问题的意外结果，并确定两个重要随机过程（即奔跑-翻滚粒子和有偏随机游走）的访问统计。
