The Spectral Gap and Convergence of Markov Chains

Abstract

There are various approaches to stochastic relaxation. In Chapter 4, we started with the conceptually and technically simplest one adopting Dobrushin’s contraction technique. Another approach is based on ‘second largest eigenvalues’ or the ‘spectral gap’. This approach applies also to processes in continuous time and space. To illustrate the ‘principal values paradigm’ we reprove the convergence theorem for homogeneous Markov chains.