Information Loss in Top to Random Shuffling

  • Authors:

  • Dudley Stark

  • Affiliations:

  • School of Mathematical Sciences, Queen Mary, University of London, London E1 4NS, UK (e-mail: D.S.Stark@maths.qmul.ac.uk)

  • Venue:
  • Combinatorics, Probability and Computing
  • Year:
  • 2002

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Abstract

A top to random shuffle of a deck of cards is performed by taking the top card off of the deck and replacing it in a randomly chosen position of the deck. We find approximations of the relative entropy of a deck of n cards after m successive top to random shuffles. Initially the relative entropy decays linearly and for larger m it decays geometrically at a rate that alters abruptly at m = n log n. It converges to an explicitly given expression when m = [n log n+cn] for a constant c.