05C50 Online Seminar: Jane Breen

Kemeny's constant is an interesting and useful quantifier of how well-connected the states of a Markov chain are. Though it was first introduced in the 1960s, interest in this concept has recently exploded.
This talk will provide an introduction to Markov chains, an overview of the history of Kemeny’s constant, discussion of some applications, and a survey of recent results, with an emphasis on those where the combinatorial structure of the Markov chain is of interest. This comes to the forefront when the Markov chain in question is a random walk on a graph, in which case Kemeny's constant is interpreted as a measure of how `well-connected' the graph is.