Information Loss in Riffle Shuffling
Published online by Cambridge University Press: 14 February 2002
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 m < log2n, and approximately exponentially for m > log2n. The deck becomes random in this information-theoretic sense after m = 3/2 log2n shuffles.
- Research Article
- Combinatorics, Probability and Computing , Volume 11 , Issue 1 , January 2002 , pp. 79 - 95
- 2002 Cambridge University Press