Path coupling without contraction

Path coupling is a useful technique for simplifying the analysis of a coupling of a Markov chain. Rather than defining and analysing the coupling on every pair in Ω ×Ω , where Ω is the state space of the Markov chain, analysis is done on a smaller set S ⊆Ω ×Ω . If the coefficient of contraction β is strictly less than one, no further analysis is needed in order to show rapid mixing. However, if β = 1 then analysis (of the variance) is still required for all pairs in Ω ×Ω . In this paper we present a new approach which shows rapid mixing in the case β = 1 with a further condition which only needs to be checked for pairs in S, greatly simplifying the work involved. We also present a technique applicable when β = 1 and our condition is not met. © 2006 Elsevier B.V. All rights reserved.