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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.