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arXiv · 1207.3406

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

Ben Morris·Weiyang Ning·Yuval Peres
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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 $Θ(n \log n)$.

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Ben Morris, Weiyang Ning, Yuval Peres. 2012-07-14. Mixing time of the Card-Cyclic-to-Random shuffle. https://arxiv.org/abs/1207.3406

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