Exact and Approximate Sampling from the Stationary Distribution of a Markov Chain

When simulating a physical system with discrete sates, one often would like to generate a sample from the stationary distribution of a Markov chain. This report focuses on three sampling methodologies which do not rely on explicitly computing the stationary distribution. Two of these lead to algorithms which can generate an exact sample in nite time. The third yields a sample whose distribution approximates, but is arbitrary close to, the stationary distribution from which one desires a sample. The approximate and one of the exact methodologies are illustrated with examples from statistical mechanics.