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