The identity is the most likely exchange shuffle for large n
Combinatorics
2018-06-19 v1
Abstract
Let a deck of n cards be shuffled by successively exchanging the cards in positions 1, 2, ..., n with cards in randomly chosen positions. We show that for n equal to 18 or greater, the identity permutation is the most likely. We prove a surprising symmetry of the resulting distribution on permutations. We also obtain the limiting distribution of the number of fixed points as n goes to infinity.
Keywords
Cite
@article{arxiv.math/0010066,
title = {The identity is the most likely exchange shuffle for large n},
author = {Daniel Goldstein and David Moews},
journal= {arXiv preprint arXiv:math/0010066},
year = {2018}
}
Comments
23+2 pages; 3 figures. Submitted to Aequationes Mathematicae