Title: From Shuffling Cards to Walking Around the Building: An Introduction to Modern Markov Chain Theory

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.

1991 Mathematics Subject Classification:

Keywords and Phrases:

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