Likelihood Orders for some Random Walks on the Symmetric Group
Combinatorics
2014-11-14 v2 Probability
Abstract
Several cycle lexicographical orders are found to describe the relative likelihood of elements of the random walks on the symmetric group generated by the conjugacy classes of transpositions, 3-cycles, and n-cycles. Spectral analysis finds sufficient time for the orders to hold. This partially answers a conjecture that the n-cycles are the least likely elements of the transposition walk on the symmetric group. A likelihood order contributes to understanding the total variation distance and separation distance for a random walk.
Cite
@article{arxiv.1306.5008,
title = {Likelihood Orders for some Random Walks on the Symmetric Group},
author = {Megan Bernstein},
journal= {arXiv preprint arXiv:1306.5008},
year = {2014}
}