Electronic Communications in Probability

Mixing Time of the Rudvalis Shuffle

David Wilson

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Abstract

We extend a technique for lower-bounding the mixing time of card-shuffling Markov chains, and use it to bound the mixing time of the Rudvalis Markov chain, as well as two variants considered by Diaconis and Saloff-Coste. We show that in each case $\Theta(n^3 \log n)$ shuffles are required for the permutation to randomize, which matches (up to constants) previously known upper bounds. In contrast, for the two variants, the mixing time of an individual card is only $\Theta(n^2)$ shuffles.

Article information

Source
Electron. Commun. Probab. Volume 8 (2003), paper no. 8, 77-85.

Dates
Accepted: 24 June 2003
First available in Project Euclid: 18 May 2016

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1463608892

Digital Object Identifier
doi:10.1214/ECP.v8-1071

Mathematical Reviews number (MathSciNet)
MR1987096

Zentralblatt MATH identifier
1061.60074

Subjects
Primary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces)
Secondary: 60C05: Combinatorial probability

Keywords
Markov chain card shuffling mixing time

Rights
This work is licensed under a Creative Commons Attribution 3.0 License.

Citation

Wilson, David. Mixing Time of the Rudvalis Shuffle. Electron. Commun. Probab. 8 (2003), paper no. 8, 77--85. doi:10.1214/ECP.v8-1071. https://projecteuclid.org/euclid.ecp/1463608892


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References

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