Geodesic
Riffle shuffles with biased cuts
Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012), DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012) (2012).

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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. 
@article{DMTCS_2012_special_263_a39,
     author = {Assaf, Sami and Diaconis, Persi and Soundararajan, Kannan},
     title = {Riffle shuffles with biased cuts},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012)},
     year = {2012},
     doi = {10.46298/dmtcs.3053},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.3053/}
}
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Assaf, Sami; Diaconis, Persi; Soundararajan, Kannan. Riffle shuffles with biased cuts. Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012), DMTCS Proceedings vol. AR, 24th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2012) (2012). doi : 10.46298/dmtcs.3053. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.3053/

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