We compute the second order correction for the cover time of the binary tree of depth n by (continuous-time) random walk, and show that with probability approaching 1 as n increases, τcov=|E|[2log2⋅n−logn/2log2+O((loglogn)8)], thus showing that the second order correction differs from the...

We consider continuous-time random interlacements on Zd, d≥3, and investigate the percolation model where a site x of Zd is occupied if the total amount of time spent at x by all the trajectories of the interlacement at level u≥0 exceeds some constant α≥0, and empty otherwise. We also...