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A transient Markov chain with finitely many cutpoints

Nicholas James, Russell Lyons, and Yuval Peres

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Abstract

We give an example of a transient reversible Markov chain that almost surely has only a finite number of cutpoints. We explain how this is relevant to a conjecture of Diaconis and Freedman and a question of Kaimanovich. We also answer Kaimanovich’s question when the Markov chain is a nearest-neighbor random walk on a tree.

Chapter information

Source
Deborah Nolan and Terry Speed, eds., Probability and Statistics: Essays in Honor of David A. Freedman (Beachwood, Ohio, USA: Institute of Mathematical Statistics, 2008), 24-29

Dates
First available in Project Euclid: 7 April 2008

Permanent link to this document
https://projecteuclid.org/euclid.imsc/1207580076

Digital Object Identifier
doi:10.1214/193940307000000365

Mathematical Reviews number (MathSciNet)
MR2459947

Zentralblatt MATH identifier
1167.60340

Subjects
Primary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces)
Secondary: 60J50: Boundary theory

Keywords
birth-and-death chain cutpoints exchangeable nearest-neighbor random walk occupation numbers transient Markov chain trees

Rights
Copyright © 2008, Institute of Mathematical Statistics

Citation

James, Nicholas; Lyons, Russell; Peres, Yuval. A transient Markov chain with finitely many cutpoints. Probability and Statistics: Essays in Honor of David A. Freedman, 24--29, Institute of Mathematical Statistics, Beachwood, Ohio, USA, 2008. doi:10.1214/193940307000000365. https://projecteuclid.org/euclid.imsc/1207580076


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References

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