Start two independent copies of a reversible Markov chain from arbitrary initial states. Then the expected time until they meet is bounded by a constant times the maximum first hitting time for the single chain. This and a sharper result are proved, and several related conjectures are discussed. © 1991.
Aldous, D. J. (1991). Meeting times for independent Markov chains. Stochastic Processes and Their Applications, 38(2), 185–193. https://doi.org/10.1016/0304-4149(91)90090-Y