一维随机游动首末返回时的初等推导
An elementary derivation of first and last return times of 1D random walks
摘要：
随机游动，特别是它们的首次通过时间，在自然界中是普遍存在的。利用路径直接计数法，我们得到了一维随机游动者的首次返回时间分布，它是一个具有无穷均值的重尾分布。使用相同的方法，我们找到了最后一个返回时间分布，它遵循反正弦定律。这两个结果在物理学和其他学科中有广泛的应用。这里提出的推导是很容易获得的物理本科生，并提供了一个基本的介绍随机游动及其有趣的性质。
英文摘要：
Random walks, and in particular, their first passage times, are ubiquitous in nature. Using direct enumeration of paths, we find the first return time distribution of a 1D random walker, which is a heavy-tailed distribution with infinite mean. Using the same method we find the last return time distribution, which follows the arcsine law. Both results have a broad range of applications in physics and other disciplines. The derivation presented here is readily accessible to physics undergraduates, and provides an elementary introduction into random walks and their intriguing properties.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
