Information loss in riffle shuffling

D Stark, AJ Ganesh, N O'Connell

Research output: Contribution to journalArticle (Academic Journal)peer-review

7 Citations (Scopus)

Abstract

We study the asymptotic behaviour of the relative entropy (to stationarity) for a commonly used model for riffle shuffling a deck of n cards m times. Our results establish and were motivated by a prediction in a recent numerical study of Trefethen and Trefethen. Loosely speaking, the relative entropy decays approximately linearly (in m) for in <log(2)n, and approximately exponentially for m > log(2) n. The deck becomes random in this information-theoretic sense after m = 3/2 log(2) n shuffles.
Translated title of the contributionInformation loss in riffle shuffling
Original languageEnglish
Pages (from-to)79 - 95
Number of pages17
JournalCombinatorics, Probability and Computing
Volume11 (1)
DOIs
Publication statusPublished - Jan 2002

Bibliographical note

Publisher: Cambridge University Press

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