# Mathematical Sciences Research Institute

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# Seminar

Mixing time of the card-cyclic to random shuffle February 28, 2012 (11:30 AM PST - 12:30 PM PST)
Parent Program: -- MSRI: Simons Auditorium
Speaker(s) Ben Morris - UC Davis
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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.

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