The derivation of the expected time to coupling in a Markov chain and its relation to the
expected time to mixing (as introduced by the author in “Mixing times with applications
to perturbed Markov chains” Linear Algebra Appl. (417, 108-123 (2006)) are explored.
The two-state cases and three-state cases are examined in detail.
Hunter, J.J. (2007), Coupling and mixing times in a Markov Chains [sic], Research Letters in the Information and Mathematical Sciences, 11, 1-22