Mixing time of the Card-Cyclic-to-Random shuffle

Ben Morris; Weiyang Ning; Yuval Peres

Mixing time of the Card-Cyclic-to-Random shuffle

Probability 2012-07-17 v1

Authors: Ben Morris , Weiyang Ning , Yuval Peres

Abstract

The Card-Cyclic-to-Random shuffle on $n$ cards is defined as follows: at time $t$ remove the card with label $t$ mod $n$ and randomly reinsert it back into the deck. Pinsky introduced this shuffle and asked how many steps are needed to mix the deck. He showed $n$ steps do not suffice. Here we show that the mixing time is on the order of $\Theta(n \log n)$ .

Keywords

card-cyclic-to-random shuffle mixing time markov chains random walks coupling total variation distance

Cite

@article{arxiv.1207.3406,
  title  = {Mixing time of the Card-Cyclic-to-Random shuffle},
  author = {Ben Morris and Weiyang Ning and Yuval Peres},
  journal= {arXiv preprint arXiv:1207.3406},
  year   = {2012}
}

Mixing time of the Card-Cyclic-to-Random shuffle

Abstract

Keywords

Cite

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