A local limit theorem for a family of non-reversible Markov chains

Details A local limit theorem for a family of non-reversible Markov chains A local limit theorem for a family of non-reversible Markov chains

2002-05-17

arxiv.org/abs/math/0205189v1

Mathematics

Probability

15 pages, 5 figures

Scientific paper

By proving a local limit theorem for higher-order transitions, we determine the time required for necklace chains to be close to stationarity. Because necklace chains, built by arranging identical smaller chains around a directed cycle, are not reversible, have little symmetry, do not have uniform stationary distributions, and can be nearly periodic, prior general bounds on rates of convergence of Markov chains either do not apply or give poor bounds. Necklace chains can serve as test cases for future techniques for bounding rates of convergence.

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