On the rate of mixing for p-shuffles

The p-shuffle is a natural generalization of the dovetail shuffle. It is de fined as follows. First, the deck is cut into a top stack and a bottom stac k 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 po ssible riffles (interleavings) of these two stacks are equally likely The m ain result of the paper is an asymptotic (N --> infinity) bound on the numb er of repetitions needed to "randomize" the deck.