Markov Chain Monte Carlo (MCMC) is a method to simulate a
desired probability distribution via constructing a Markov chain whose
stationary distribution is the one we are looking for. Mixing time
describes the rate of convergence of a Markov chain to its stationary
distribution. We will give examples of Gibbs sampling algorithms (also
known as Glauber dynamics). We will explain how strong stationary time
and coupling are used to obtain bounds on mixing time. We will also
discuss new approaches to coupling method and their applications.
