An Analysis of the Diaconis-Holmes-Neal Markov Chain Sampler Under Generalized Unimodal Underlying Probabilities

Upon the introduction of the Metropolis algorithm, the question of how many steps in the Markov chain were needed to achieve convergence to stationarity became apparent. The convergence was rather slow, i.e. for a process on $n$ states the number of steps needed to achieve convergence to stationarit