On the rate of mixing for p-shuffles

The p-shuffle is a natural generalization of the dovetail shuffle. It is defined as follows. First, the deck is cut into a top stack and a bottom stack so that the distribution of the size of the top stack is Binomial (N,p), where N is the total number of cards in the deck.Then, conditional on the outcome of the cut,the two stacks are .riffled. in such a way that all possible riffles (interleavings) of these two stacks are equally likely. The main result of the paper is an asymptotic (N..) bound on the number of repetitions needed to .randomize. the deck.