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.
Technical Report BU-1385-M, Biometrics Unit, Cornell University, 26 pages: postscript, pdf.
Diaconis, P., Holmes, S., and Neal, R. M. (2000) ``Analysis of a nonreversible Markov chain sampler'', Annals of Applied Probability, vol. 10, pp. 726-752: abstract.