An elementary derivation of first and last return times of 1D random walks

Sarah Kostinski, Ariel Amir

Research output: Contribution to journalArticlepeer-review

Abstract

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 one-dimensional 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.
Original languageEnglish
Pages (from-to)57-60
Number of pages4
JournalAmerican Journal of Physics
Volume84
Issue number1
Early online date22 Dec 2015
DOIs
StatePublished - Jan 2016
Externally publishedYes

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