Electronic Communications in Probability

Mixing Time of the Rudvalis Shuffle

David Wilson

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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

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

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

Markov chain card shuffling mixing time

This work is licensed under aCreative Commons Attribution 3.0 License.


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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