Total variation cutoff for the transpose top-$2$ with random shuffle
Probability
2021-01-05 v2
Abstract
In this paper, we investigate the properties of a random walk on the alternating group generated by -cycles of the form and . We call this the transpose top- with random shuffle. We find the spectrum of the transition matrix of this shuffle. We show that the mixing time is of order and prove that there is a total variation cutoff for this shuffle.
Keywords
Cite
@article{arxiv.1807.08539,
title = {Total variation cutoff for the transpose top-$2$ with random shuffle},
author = {Subhajit Ghosh},
journal= {arXiv preprint arXiv:1807.08539},
year = {2021}
}
Comments
22 pages, 1 table, 1 figure. Minor revisions. The main result (Theorem 3.2 in the older version) has been stated (Theorem 1.1 in the updated version) in the introduction. The link between $P$ and the Jucys Murphy elements has been presented in Lemma 2.1. Examples of Corollary 2.6 have been given in section 2. The figure has been updated from $n=8$ to $n=10$. Some minor changes are done