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

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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]
Copyright of American Journal of Physics is the property of American Institute of Physics and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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Header DbId: egs
DbLabel: Engineering Source
An: 111950567
AccessLevel: 6
PubType: Academic Journal
PubTypeId: academicJournal
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  Data: An elementary derivation of first and last return times of 1D random walks.
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  Data: <searchLink fieldCode="AR" term="%22Kostinski%2C+Sarah%22">Kostinski, Sarah</searchLink><relatesTo>1</relatesTo><i> skostinski@physics.harvard.edu</i><br /><searchLink fieldCode="AR" term="%22Amir%2C+Ariel%22">Amir, Ariel</searchLink><relatesTo>2</relatesTo><i> arielamir@seas.harvard.edu</i>
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  Data: <searchLink fieldCode="JN" term="%22American+Journal+of+Physics%22">American Journal of Physics</searchLink>. Jan2016, Vol. 84 Issue 1, p57-60. 4p.
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  Data: <searchLink fieldCode="DE" term="%22Random+walks%22">Random walks</searchLink><br /><searchLink fieldCode="DE" term="%22Arcsine+function%22">Arcsine function</searchLink><br /><searchLink fieldCode="DE" term="%22Distribution+%28Probability+theory%29%22">Distribution (Probability theory)</searchLink><br /><searchLink fieldCode="DE" term="%22Physics%22">Physics</searchLink><br /><searchLink fieldCode="DE" term="%22Undergraduates%22">Undergraduates</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: 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]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of American Journal of Physics is the property of American Institute of Physics and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1119/1.4930092
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        Text: English
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      – SubjectFull: Arcsine function
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      – SubjectFull: Distribution (Probability theory)
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              Text: Jan2016
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