Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-27T22:29:53.030Z Has data issue: false hasContentIssue false
  • English
  • Français

Information Loss in Top to Random Shuffling

Published online by Cambridge University Press:  21 November 2002

DUDLEY STARK
DUDLEY STARK
Affiliation:
School of Mathematical Sciences, Queen Mary, University of London, London E1 4NS, UK (e-mail: D.S.Stark@maths.qmul.ac.uk)
Get access Rights & Permissions [Opens in a new window]

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.

Type
Research Article
Information
Combinatorics, Probability and Computing , Volume 11 , Issue 6 , November 2002 , pp. 607 - 627
Copyright
2002 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)