Berry-type conjecture for eigenfunctions on expanding locally symmetric spaces

Let $X$ be the universal symmetric space and let $(M_n=\Gamma_n\backslash X)$ be a uniformly discrete expander family that BS-converges toward $X$. Fix an eigenvalue $\lambda_0$ of the Laplace operator on $L^2(X)$, and let $\delta_n\to0$ be the sequence supplied by the Weyl-law proposition. Consider all eigenfunctions $\phi_j^{(n)}$ with eigenvalues $\lambda_j^{(n)}\in[\lambda_0-\delta_n,\lambda_0+\delta_n]$. Berry-type conjecture for expander families. The collection of pairs $\{(M_n,\phi_j^{(n)}):\lambda_j^{(n)}\in[\lambda_0-\delta_n,\lambda_0+\delta_n]\}$ is relatively compact in the BS topology; its accumulation points are random fields on $X$, and the only possible aperiodic accumulation point is the isotropic monochromatic Gaussian random wave on $X$ with eigenvalue $\lambda_0$. This is a locally symmetric-space analogue of Berry's conjecture, motivated by results on eigenvectors of random regular graphs; the source presents it as provocative and does not state a resolution.