Originally, quantum ergodicity concerned equidistribution properties of Laplacian eigenfunctions with large eigenvalue on manifolds for which the geodesic flow is ergodic. 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 and when one restricts to eigenfunctions with eigenvalues in a fixed range. Following the breakthrough work of Anantharaman-Le Masson '15 on this type of quantum ergodicity on regular graphs, previous authors have also considered rank one locally symmetric spaces and some higher rank locally symmetric spaces. We prove analogous results in the case when the underlying common universal cover is the Bruhat-Tits building associated to PGL(3) over 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. We shall also mention ongoing joint work with Farrell Brumley, Simon Marshall, and Jasmin Matz dealing further with higher rank locally symmetric spaces.
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Pré-séminaire 13h30 par Bertrand Rémy.
