English

Riffle shuffles with biased cuts

Probability 2011-12-13 v1

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.

Keywords

Cite

@article{arxiv.1112.2650,
  title  = {Riffle shuffles with biased cuts},
  author = {Sami Assaf and Persi Diaconis and Kannan Soundararajan},
  journal= {arXiv preprint arXiv:1112.2650},
  year   = {2011}
}

Comments

10 pages

R2 v1 2026-06-21T19:49:59.427Z