Benjamini–Lyons–Peres–Schramm conjecture on bushes along a uniform spanning forest ray

Let $T_{0}$ be the component of the origin in the uniform spanning forest on $\mathbb{Z}^{d}$, and let $\xi$ be the unique infinite ray from $0$ in $T_{0}$. The Benjamini–Lyons–Peres–Schramm conjecture. The sequence of “bushes” observed along $\xi$ converges in distribution. This conjecture concerns the local structure encountered along the infinite ray in a component of the uniform spanning forest. The supplied text attributes it to Benjamini, Lyons, Peres, and Schramm, but gives no resolution status.