2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/161102We 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.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)Probability60J10 (Primary) 60J50 (Secondary)text