论文标题
一维随机步行的完整访问统计数据
Complete Visitation Statistics of 1d Random Walks
论文作者
论文摘要
我们开发了一个框架，以确定随机步行理论中基本数量的完整统计行为，即$ n_1 $，$ n_2 $，$ n_3 $，。 。 。有时会访问不同的站点，$ t_1 $，$ t_2 $，$ t_3 $，...。从这个多个时间分布中，我们表明，一维随机步行的访问统计在时间上相关，我们量化了该过程的非马克维亚性质。我们利用这些想法为两次陷阱问题得出意外的结果，并确定两个重要的随机过程的访问统计数据，即运行式的粒子和有偏见的随机步行。
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 1d 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 also to determine the visitation statistics of two important stochastic processes, the run-and-tumble particle and the biased random walk.
