Linear Cover Time is Exponentially Unlikely
Probability
2010-11-16 v1 Combinatorics
Abstract
We show that the probability that a simple random walk covers a finite, bounded degree graph in linear time is exponentially small. More precisely, for every D and C, there exists a=a(D,C)>0 such that for any graph G, with n vertices and maximal degree D, the probability that a simple random walk, started anywhere in G, will visit every vertex of G in its first Cn steps is at most exp(-an). We conjecture that the same holds for a=a(C)>0 that does not depend on D, provided that the graph G is simple.
Cite
@article{arxiv.1011.3118,
title = {Linear Cover Time is Exponentially Unlikely},
author = {Itai Benjamini and Ori Gurel-Gurevich and Ben Morris},
journal= {arXiv preprint arXiv:1011.3118},
year = {2010}
}
Comments
11 pages