Peskun ordering is a partial ordering defined on the space of transition matrices of discrete time Markov chains. If the Markov chains are reversible with respect to a common stationary distribution "greek Pi", Peskun ordering implies an ordering on the asymptotic variances of the resulting...

If T is the coalescence time of the Propp and Wilson, perfect simulation algorithm, the aim of this paper is to show that T depends on the second largest eigenvalue modulus of the transition matrix of the underlying Markov chain. This gives a relationship between the ordering based on the speed...