Riffle shuffles with biased cuts

Details Riffle shuffles with biased cuts Riffle shuffles with biased cuts

2011-12-12

arxiv.org/abs/1112.2650v1

Mathematics

Probability

10 pages

Scientific paper

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.

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