Abstract
We introduce a new partial order on the class of stochastically monotone Markov kernels having a given stationary distribution
Using comparison inequalities together with specialized arguments to remove the stochastic monotonicity restriction, we answer a question of Persi Diaconis by showing that, among all symmetric birth-and-death kernels on the path
We also use comparison inequalities:
(i) to identify, when
(ii) to recover and extend a result of Peres and Winkler that extra updates do not delay mixing for monotone spin systems.
Among the fastest-mixing chains in (i), we show that the chain for uniform
Citation
James Allen Fill. Jonas Kahn. "Comparison inequalities and fastest-mixing Markov chains." Ann. Appl. Probab. 23 (5) 1778 - 1816, October 2013. https://doi.org/10.1214/12-AAP886
Information