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Mixing Time of the Rudvalis Shuffle

   
@article{ECP1071,
	author = {David Wilson},
	title = {Mixing Time of the Rudvalis Shuffle},
	journal = {Electron. Commun. Probab.},
	fjournal = {Electronic Communications in Probability},
	volume = {8},
	year = {2003},
	keywords = {Markov chain, card shuffling, mixing time},
	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.},
	pages = {no. 8, 77-85},
	issn = {1083-589X},
	doi = {10.1214/ECP.v8-1071},    
        url = {http://ecp.ejpecp.org/article/view/1071}}