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Analysis of Top To Random Shuffles

Published online by Cambridge University Press:  12 September 2008

Persi Diaconis ,
James Allen Fill  and
Jim Pitman
Persi Diaconis
Affiliation:
Dept. of Mathematics, Harvard University, Cambridge, MA 02138
James Allen Fill
Affiliation:
Dept. of Mathematical Sciences, The Johns Hopkins University, Baltimore, MD 21218–2689
Jim Pitman
Affiliation:
Dept. of Statistics, University of California, Berkeley, CA 94720
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Abstract

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.

Type
Research Article
Information
Combinatorics, Probability and Computing , Volume 1 , Issue 2 , June 1992 , pp. 135 - 155
Copyright
Copyright © Cambridge University Press 1992

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