A spectral characterization for concentration of the cover time
Probability
2019-12-24 v3
Abstract
We prove that for a sequence of finite vertex-transitive graphs of increasing sizes, the cover times are asymptotically concentrated if and only if the product of the spectral-gap and the expected cover time diverges. In fact, we prove this for general reversible Markov chains under the much weaker assumption (than transitivity) that the maximal hitting time of a state is of the same order as the average hitting time.
Keywords
Cite
@article{arxiv.1809.00145,
title = {A spectral characterization for concentration of the cover time},
author = {Jonathan Hermon},
journal= {arXiv preprint arXiv:1809.00145},
year = {2019}
}
Comments
19 pages. Some typos were fixed in this version