## The Annals of Applied Probability

### Mixing time of the card-cyclic-to-random shuffle

#### 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 Unpublished manuscript] introduced this shuffle and asked how many steps are needed to mix the deck.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 $\Theta(n\log n)$.

#### Article information

Source
Ann. Appl. Probab., Volume 24, Number 5 (2014), 1835-1849.

Dates
First available in Project Euclid: 26 June 2014

https://projecteuclid.org/euclid.aoap/1403812363

Digital Object Identifier
doi:10.1214/13-AAP964

Mathematical Reviews number (MathSciNet)
MR3226165

Zentralblatt MATH identifier
1321.60143

Keywords
Markov chain mixing time

#### Citation

Morris, Ben; Ning, Weiyang; Peres, Yuval. Mixing time of the card-cyclic-to-random shuffle. Ann. Appl. Probab. 24 (2014), no. 5, 1835--1849. doi:10.1214/13-AAP964. https://projecteuclid.org/euclid.aoap/1403812363

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