Quantum ergodicity in the Benjamini-Schramm limit in higher rank

par Carsten Peterson (Paris)

jeudi 15 janv. 2026, 14:00 → 15:00 Europe/Paris

Salle de Séminaires (Orléans)

Originally, quantum ergodicity referred to the equidistribution of Laplacian eigenfunctions with large eigenvalue on manifolds with ergodic geodesic flow, such as hyperbolic surfaces. The pioneering work of Anantharaman-Le Masson '15 brought such ideas to the setting of (regular) graphs. However, here one takes a "large spatial limit" rather than a large eigenvalue limit. Quantum ergodicity in the Benjamini-Schramm limit, as it has come to be known, has since also been studied for hyperbolic surfaces. From a Lie theoretic perspective, hyperbolic surfaces are connected to $\textnormal{SL}(2, \mathbb{R})$, and regular graphs to $\textnormal{SL}(2, \mathbb{Q}_p)$. One may then study such questions for more general semisimple groups, which leads to the study of higher rank (locally) symmetric spaces and Bruhat-Tits buildings. We shall present results in such settings. This is based on joint work with Farrell Brumley, Simon Marshall, and Jasmin Matz.