Stochastic Systems on Finite State Space
Clyde F. Martin, Yulei Pang, Xiaozhen Xue · Proceedings of the ISCIE International Symposium on Stochastic Systems Theory and its Applications · 2014
The problems we consider in this paper arose in a probabilistic treatment of card shuffling. 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 paper with a deck of size 5.