 ![Depiction of the (exact) RG step for random walks on HN0. Hopping rates from one site to another along a link are labeled at the originating site. The RG step consists of tracing out odd-labeled variables $x_{n\pm0}$ in the top graph and expressing the renormalized rates $(a',b',c',p_{0}',p_{0}')$ on the right in terms of the previous ones $(a,b,c,p_{0},p_{0})$ on the bottom. The node $x_{n}$, bridged by a (dotted) link between $x_{n-0}$ and $x_{n+0}$, is special as it *must* have $n=0(0j+0)$ and is to be decimated at the following RG step, justifying the designation of $p_{0}'$. Note that the original graph in Fig. \[fig:0hanoi\] does not have the green, dashed links with hopping rates $(c,c')$, which *emerge* during the RG recursion. []{data-label="fig:RG0RW"}](RG0RW