Mixing Time of the Rudvalis Shuffle
Probability
2012-06-26 v1
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.
Cite
@article{arxiv.math/0210469,
title = {Mixing Time of the Rudvalis Shuffle},
author = {David Bruce Wilson},
journal= {arXiv preprint arXiv:math/0210469},
year = {2012}
}
Comments
9 pages