Microlocal quantum unique ergodicity for paths on the Bruhat–Tits graph

Fix $n\in\mathbb{Z}_{\geqslant 0}$ and let $N\geqslant n$ tend to infinity. Let $\mathbf{Y}_{-N..N}$ be the space of paths used above, let $\mathcal{F}_{-N..N}$ be the specified family of Hecke eigenfunctions on this space, and for $\varphi\in\mathcal{F}_{-N..N}$ let $\mu_\varphi$ be the probability measure on $\mathbf{Y}_{-n..n}$ defined by pushforward and averaging $|\varphi|^2$. Microlocal quantum unique ergodicity conjecture. In the context of Question, the uniform measure on $\mathbf{Y}_{-n..n}$ is the only possible weak limit: for any sequence $\varphi_N\in\mathcal{F}_{-N..N}$ and any $E\subseteq\mathbf{Y}_{-n..n}$,

$$\lim_{N\rightarrow\infty}\mu_{\varphi_N}(E)=\frac{|E|}{|\mathbf{Y}_{-n..n}|}.$$

This is presented as an analogue of the arithmetic quantum unique ergodicity conjecture of Rudnick–Sarnak; the source says it had not appeared explicitly in the literature and does not provide a resolution.