Yulei Pang (Texas Tech University)

Title: Random walks and cards shuffling

Abstract: In this poster arose in a probabilistic treatment of card shuffling. We use top-in shuffle and transposition shuffle as examples. However we treat them as stochastic discrete time switching systems. When a deck of n cards is used the state space has n! elements so that for even small n the problem becomes very difficult to handle. We show that we can reduce the dimension of the state space first to the number of partitions n into non-negative integer parts and then using this we reduce the state space to size n for a particular type of shuffle. We demonstrate the procedure in this poster with a deck of size 5. We also address the question "for a deck of cards, how many times a top-in shuffle should be performed before the top card goes back to the original position?" This problem has been studied in the literature but we are interested in the implications for linear switching systems.