Invariant distribution: properties and examples

This lecture covers the properties of invariant distributions in Markov chains, focusing on positive recurrent communicating classes. The instructor proves the existence and uniqueness of invariant distributions, supported by communicating classes. The lecture discusses the convergence of distributions and the concept of aperiodicity in Markov chains. Examples include random walks on finite cubes and the convergence theorem for irreducible aperiodic positive recurrent matrices.