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From shuffling cards to walking around the building: An introduction to modern Markov chain theory. (English) Zbl 0902.60052

Summary: 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.

MSC:

60G50 Sums of independent random variables; random walks
60C05 Combinatorial probability
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