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Mixing Times for Markov Chains on Wreath Products and Related Homogeneous Spaces

   
@article{EJP84,
	author = {James Fill and Clyde Schoolfield, Jr.},
	title = {Mixing Times for Markov Chains on Wreath Products and Related Homogeneous Spaces},
	journal = {Electron. J. Probab.},
	fjournal = {Electronic Journal of Probability},
	volume = {6},
	year = {2001},
	keywords = {Markov chain, random walk, rate of convergence to stationarity, mixing time, wreath product, Bernoulli-Laplace diffusion, complete monomial group, hyperoctahedral group, homogeneous space, Möbius inversion.},
	abstract = {We develop a method for analyzing the mixing times for a  quite general class of Markov chains on the complete monomial group $G \wr S_n$ 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.},
	pages = {no. 11, 1-22},
	issn = {1083-6489},
	doi = {10.1214/EJP.v6-84},    
        url = {http://ejp.ejpecp.org/article/view/84}}