4 problems

Convergence conjecture.

Let $\mathbb L_n$ be the set of vertices at level $n$ of the rooted regular tree with branching factor $b$, let $L_t(x)$ denote the local time at vertex $x$ up to time $t$ for simp…

Let $\mathbb{T}_{d}$ be the homogeneous $d$-ary tree with $d\geq 3$, and let ${\mathbf a}$ be an $L$-periodic rotor sequence. The regular-tree uniform-shift transience conjecture.…

Let $\mathbb{T}_{2}$ be the binary tree, and let ${\mathbf a}$ be an $L$-periodic rotor sequence. Define $\mathcal{A}_{\mathrm{rec}}^{\mathrm{conj}}$ to consist of all shifts of se…