Bibliographic Details
| Title: |
An elementary derivation of first and last return times of 1D random walks. |
| Authors: |
Kostinski, Sarah1 skostinski@physics.harvard.edu, Amir, Ariel2 arielamir@seas.harvard.edu |
| Source: |
American Journal of Physics. Jan2016, Vol. 84 Issue 1, p57-60. 4p. |
| Subjects: |
Random walks, Arcsine function, Distribution (Probability theory), Physics, Undergraduates |
| 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. [ABSTRACT FROM AUTHOR] |
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| Database: |
Engineering Source |
