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 [Probabilistic and combinatorial aspects of the card-cyclic-to-random shuffle (2011). Unpublished manuscript] introduced this shuffle and asked how many steps are needed to mix the deck.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 $\Theta(n\log n)$.
Citation
Ben Morris. Weiyang Ning. Yuval Peres. "Mixing time of the card-cyclic-to-random shuffle." Ann. Appl. Probab. 24 (5) 1835 - 1849, October 2014. https://doi.org/10.1214/13-AAP964
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