Mixing Times for Markov Chains on Wreath Products and Related Homogeneous Spaces
James Allen Fill, The Johns Hopkins University
Clyde H. Schoolfield, Jr., Harvard University
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 Sn and a quite general class of Markov chains
on the homogeneous space (G wr Sn) / (Sr times
Sn-r).
We derive an exact formula for the L2 distance in terms of
the L2 distances to uniformity for closely related random
walks on the symmetric groups Sj for 1 leq j leq n
or for closely related Markov chains on the homogeneous spaces
Si+j / (Si times Sj) 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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