A transient Markov chain with finitely many cutpoints

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.Comment: Published in at http://dx.doi.org/10.1214/193940307000000365 the IMS Collections (http://www.imstat.org/publications/imscollections.htm) by the Institute of Mathematical Statistics (http://www.imstat.org