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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 rununtil the time $uN^d$. We prove that for all $d\ge 3$ and $u>0$, the mixingtime for the random walk on this subgraph is of order $N^2$ with probability atleast $1 - Ce^{-(\log N)^2}$.

Mixing time for the random walk on the range of the random walk on tori