The general theory implies that the distribution of an irreducible Markov chain converges to its stationary distribution as time diverges to infinity. The speed of corresponding convergence is a significant issue in the study of mathematical physics or statistical technique known as MCMC. In particular, this speed is exponentially slow under the presence of metastability. In this presentation, we shall focus on the other case; absence of metastability. We will observe a peculiar behavior known as the cut-off phenomenon.
