Introduction to Markov Chains

The aims of this book are threefold: We start with a naive description of a Markov chain as a memoryless random walk on a finite set. This is complemented by a rigorous definition in the framework of probability theory, and then we develop the most important results from the theory of homogeneous Markov chains on finite state spaces. Chains are called rapidly mixing if all of the associated walks, regardles of where they started, behave similarly already after comparitively few steps: it is impo