Cutoff for the asymmetric riffle shuffle
Cutoff for the asymmetric riffle shuffle
In the Gilbert–Shannon–Reeds shuffle, a deck of N cards is cut into two approximately equal parts which are riffled together uniformly at random. Bayer and Diaconis (Ann. Appl. Probab. 2 294–313) famously showed that this Markov chain undergoes cutoff in total variation after 3log(N) 2log(2) shuffles. We establish cutoff for …