Abstract: Originally, quantum ergodicity concerned equidistribution properties of Laplacian eigenfunctions with large eigenvalue on manifolds for which the geodesic flow is ergodic (such as hyperbolic surfaces). More recently, several authors have investigated quantum ergodicity for sequences of spaces which ``converge'' (in the sense of Benjamini-Schramm) to their common universal cover (such as a sequence of hyperbolic surfaces whose injectivity radii go to infinity) and when one restricts to eigenfunctions with eigenvalues in a fixed range. Previous authors have considered this type of quantum ergodicity in the settings of regular graphs, rank one symmetric spaces, and some higher rank symmetric spaces. We prove analogous results in the case when the underlying common universal cover is the Bruhat-Tits building associated to $PGL(3, F)$ where $F$ is a non-archimedean local field. This may be seen as both a higher rank analogue of the regular graphs setting as well as a non-archimedean analogue of the symmetric space setting.

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https://umich.zoom.us/j/91432197415?pwd=MmtGVmwwUFFUTGlVclphM1NLbjBoZz09