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3 - Markov Chains

from Part I - Tools and Theory

Published online by Cambridge University Press:  16 May 2024

Ariel Yadin
Ariel Yadin
Affiliation:
Ben-Gurion University of the Negev, Israel
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Summary

In this chapter the basic theory of Markov chains is developed, with a focus on irreducible chains.The transition matrix is introduced as well as the notions of irreducibility, periodicity, recurrence (null and positive), and transience.The theory is applied to the relationship of a random walk on a group to the random walk on a finite-index subgroup induced by the "hitting measure."

Keywords

Markov chainirreducible Markov chaintransition matrixrandom walk on a groupstopping timesrecurrencetransience
Type
Chapter
Information
Harmonic Functions and Random Walks on Groups , pp. 75 - 116
Publisher: Cambridge University Press
Print publication year: 2024

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  • Markov Chains
  • Ariel Yadin, Ben-Gurion University of the Negev, Israel
  • Book: Harmonic Functions and Random Walks on Groups
  • Online publication: 16 May 2024
  • Chapter DOI: https://doi.org/10.1017/9781009128391.005
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  • Markov Chains
  • Ariel Yadin, Ben-Gurion University of the Negev, Israel
  • Book: Harmonic Functions and Random Walks on Groups
  • Online publication: 16 May 2024
  • Chapter DOI: https://doi.org/10.1017/9781009128391.005
Available formats
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Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • Markov Chains
  • Ariel Yadin, Ben-Gurion University of the Negev, Israel
  • Book: Harmonic Functions and Random Walks on Groups
  • Online publication: 16 May 2024
  • Chapter DOI: https://doi.org/10.1017/9781009128391.005
Available formats
×