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Analysis of Top To Random Shuffles

  • Persi Diaconis (a1), James Allen Fill (a2) and Jim Pitman (a3)


A deck of n cards is shuffled by repeatedly taking off the top m cards and inserting them in random positions. We give a closed form expression for the distribution after any number of steps. This is used to give the asymptotics of the approach to stationarity: for m fixed and n large, it takes shuffles to get close to random. The formulae lead to new subalgebras in the group algebra of the symmetric group.



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Combinatorics, Probability and Computing
  • ISSN: 0963-5483
  • EISSN: 1469-2163
  • URL: /core/journals/combinatorics-probability-and-computing
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