Cutoff for the asymmetric riffle shuffle

Mon October 18th 2021, 4:00pm
Sequoia 200
Mark Sellke, Stanford Math

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. This Markov chain famously undergoes total variation cutoff after (3/2)*log_2(N) shuffles. We prove cutoff for asymmetric riffle shuffles in which the deck is cut into differently sized parts before riffling, confirming a conjecture of Lalley from 2000.