Riffle shuffles with biased cuts

Sami Assaf; Persi Diaconis; Kannan Soundararajan

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arXiv · 1112.2650

Riffle shuffles with biased cuts

Sami Assaf·Persi Diaconis·Kannan Soundararajan

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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.

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Sami Assaf, Persi Diaconis, Kannan Soundararajan. 2011-12-12. Riffle shuffles with biased cuts. https://arxiv.org/abs/1112.2650

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