Mathematics – Probability
Scientific paper
2000-06-09
Mathematics
Probability
25 pages. See also http://www.mts.jhu.edu/~fill/ and http://www.fas.harvard.edu/~chschool/ . Submitted for publication in May,
Scientific paper
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.
Jr.
Fill James Allen
Schoolfield Clyde H.
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