Mixing times for Markov chains on wreath products and related homogeneous spaces

James Allen Fill; Clyde H. Schoolfield, Jr.

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arXiv · math/0006076

Mixing times for Markov chains on wreath products and related homogeneous spaces

James Allen Fill·Clyde H. Schoolfield, Jr.

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Abstract

We develop a method for analyzing the mixing times for a quite general class of Markov chains on the complete monomial group G \wr S_n (the wreath product of a group G with the permutation group S_n) and a quite general class of Markov chains on the homogeneous space (G \wr S_n) / (S_r \times S_{n - r}). We derive an exact formula for the L^2 distance in terms of the L^2 distances to uniformity for closely related random walks on the symmetric groups S_j for 1 \leq j \leq n or for closely related Markov chains on the homogeneous spaces S_{i + j} / (S_i \times S_j) for various values of i and j, respectively. Our results are consistent with those previously known, but our method is considerably simpler and more general.

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James Allen Fill, Clyde H. Schoolfield, Jr.. 2000-06-09. Mixing times for Markov chains on wreath products and related homogeneous spaces. https://arxiv.org/abs/math/0006076

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