# Mathematics Colloquia and Seminars

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

**Mathematical Physics & Probability**

Speaker: | Ben Morris, UC Davis |

Location: | 1147 MSB |

Start time: | Wed, Oct 31 2012, 4:10PM |

We analyze the following method for shuffling n cards. First, remove card 1 (i.e., the card with label 1) and then re-insert it randomly into the deck. Then repeat with cards 2, 3,..., n. Call this a round. R. Pinsky showed, somewhat surprisingly, that the mixing time is greater than one round. We show that in fact the mixing time is on the order of log n rounds. Joint work with Weiyang Ning and Yuval Peres.