From shuffling cards to walking around the building: An introduction to modern Markov chain theory

  • Persi Diaconis


This paper surveys recent progress in the classical subject of Markov chains. Sharp rates of convergence are available for many chains. Examples include shuffling cards, a variety of simulation procedures used in physics and statistical work, and random walk on the chambers of a building. The techniques used are a combination of tools from geometry, PDE, group theory and probability.