Coupling and Mixing in Markov chains
by
Jeffrey Hunter
Auckland University of Technology

Following a discussion of the concepts of mixing and coupling in Markov chains, expressions for the expected times to mixing and coupling are developed. The two-state cases and three-state cases are examined in detail and some results for the bounds on the expected values are given. The key results are given in Hunter, J.J.: “Coupling and mixing times in a Markov chain”, Linear Algebra and its Applications, 430, 2607-2621, (2009), and Hunter, J.J.: “Bounds on Expected Coupling Times in a Markov Chain”, (pp271-294), “Statistical Inference, Econometric Analysis and Matrix Algebra. Festschrift in Honour of Götz Trenkler”, Bernhard Schipp and Walter Krämer (Editors), Physica-Verlag Heidelberg 2009)

Date received: December 5, 2009