2011/12/12 by Assaf, Sami, Diaconis, Persi, Soundararajan, Kannan
#60B15 #60C05 #FOS: Mathematics #Probability (math.PR)
paper · doi:10.48550/arxiv.1112.2650
The well-known Gilbert-Shannon-Reeds model for riffle shuffles assumes that the cards are initially cut 'about in half' and then riffled together. We analyze a natural variant where the initial cut is biased. Extending results of Fulman (1998), we show a sharp cutoff in separation and L-infinity distances. This analysis is possible due to the close connection between shuffling and quasisymmetric functions along with some complex analysis of a generating function.