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 for more general asymmetric riffle shuffles one cuts differently sized parts. The value point confirms conjecture Lalley from 2000 10 1302–1321). Some appealing consequences asymmetry always slows mixing strictly faster than separation L∞ mixing.