Analysis of a nonreversible Markov chain speedup by a single edge
Abstract
We present a Markov chain example where nonreversibility and an added edge jointly improve mixing time: when a random edge is added to a cycle of $n$ vertices and a Markov chain with a drift is introduced, we get mixing time of $O(n^{3/2})$ with probability bounded away from 0. If only one of the two modifications were performed, the mixing time would stay $\Omega(n^2)$.
 Publication:

arXiv eprints
 Pub Date:
 May 2019
 arXiv:
 arXiv:1905.03223
 Bibcode:
 2019arXiv190503223G
 Keywords:

 Mathematics  Probability;
 60J10;
 37A25
 EPrint:
 15 pages, 5 figures