The Cutoff Phenomenon for Families of Finite Ergodic Markov Chains

Abstract

We study the cutoff phenomenon for several families of finite ergodic Markov chains. The cutoff phenomenon describes the asymptotically abrupt convergence of a family of processes towards their stationary distribution at deterministic times. We introduce the cutoff phenomenon intuitively by familiarising the reader with the basic theory behind Markov chains followed by an illustrative example. After this, we provide the reader with a formal definition of the cutoff phenomenon and discuss different models of increasing complexity exhibiting cutoff. For the models we consider, several techniques turn out to be useful to prove the exhibition of cutoff.