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Information Center for Mathematical Science

PAC

Information Center for Mathematical Science

PAC

Riffle shuffles with biased cuts
Author Persi Diaconis (Stanford University)
Homepage Url http://www-stat.stanford.edu/~cgates/PERSI/year.html
Coauthors Sami Assaf, Kannan Soundararajan
Abstract 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.
Abstract Url http://www-stat.stanford.edu/~cgates/PERSI/papers/fpsac_biased-1.pdf