We analyse the convergence to stationarity of a simple non-reversible Markov chain that serves as a model for several non-reversible Markov chain sampling methods that are used in practice. Our theoretical and numerical results show that non-reversibility can indeed lead to improvements over the diffusive behavior of simple Markov chain sampling schemes. The analysis uses both probabilistic techniques and an explicit diagonalisation.
Annals of Applied Probability, vol. 10, pp. 726-752 (2000).
Diaconis, P., Holmes, S., and Neal, R. M. (1997) ``Analysis of a non-reversible Markov chain sampler'', Technical Report BU-1385-M, Biometrics Unit, Cornell University, 26 pages: abstract, postscript, pdf.