Electronic Journal of Probability

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

James Fill and Clyde Schoolfield, Jr.

Full-text: Open access

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.

Article information

Source
Electron. J. Probab., Volume 6 (2001), paper no. 11, 22 pp.

Dates
Accepted: 23 April 2001
First available in Project Euclid: 19 April 2016

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1461097641

Digital Object Identifier
doi:10.1214/EJP.v6-84

Mathematical Reviews number (MathSciNet)
MR1831806

Zentralblatt MATH identifier
0976.60069

Subjects
Primary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces) 60B10: Convergence of probability measures
Secondary: 20E22: Extensions, wreath products, and other compositions [See also 20J05]

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

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

Fill, James; Schoolfield, Jr., Clyde. Mixing Times for Markov Chains on Wreath Products and Related Homogeneous Spaces. Electron. J. Probab. 6 (2001), paper no. 11, 22 pp. doi:10.1214/EJP.v6-84. https://projecteuclid.org/euclid.ejp/1461097641


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References

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