Ebook: Markov chains and mixing times

Introduction to finite Markov chains --

Classical (and useful) Markov chains --

Markov chain Monte Carlo : metropolis and Glauber chains --

Introduction to Markov chain mixing --

Coupling --

Strong stationary times --

Lower bounds on mixing times --

The symmetric group and shuffling cards --

Random walks on networks --

Hitting times --

Cover times --

Eigenvalues --

Eigenfunctions and comparison of chains --

The transportation metric and path coupling --

The Ising model --

From shuffling cards to shuffling genes --

Martingales and evolving sets --

The cutoff phenomenon --

Lamplighter walks --

Continuous-time chains --

Countable state space chains --

Coupling from the past --

Open problems --

Appendix A : Background material --

Appendix B : Introduction to simulation