Comparison inequalities and fastest-mixing Markov chains (Q373832)

From the authors' abstract: The authors introduce a new partial order on the class of stochastically monotone Markov kernels having a given stationary distribution on a given finite partially ordered state space. Using comparison inequalities together with specialized arguments to remove the stochastic monotonicity restriction, they answer a question of Persi Diaconis about fastest convergence among all symmetric birth-and-death kernels. They also use comparison inequalities for fastest-mixing Markov chains.