TITLE: What is the cover time of a random walk on a cube?
QUESTION [11 upvotes]: I can't quite figure this problem yet. There is an ant at one vertex of a cube. The ant goes from one vertex to another by choosing one of the neighboring vertices uniformly at random. What is the average minimum time it takes to visit all vertices?

REPLY [6 votes]: Yet another reference: Some sample path properties of a random walk on the cube, by Peter Matthews (1989). This covers the asymptotic distribution of the time $T$ taken to visit all vertices, the distribution of the number of vertices not visited at times near to $\mathbb{E}[T]$, and the expected time taken for the walk to come within a distance $d$ of all vertices.