  Consider the subgraph of the discrete $d$-dimensional torus of size length
$N$, $d\ge3$, induced by the range of the simple random walk on the torus run
until the time $uN^d$. We prove that for all $d\ge 3$ and $u>0$, the mixing
time for the random walk on this subgraph is of order $N^2$ with probability at
least $1 - Ce^{-(\log N)^2}$.
