Séminaire Orléans
Quantum ergodicity in the Benjamini-Schramm limit in higher rankCarsten Peterson (Paris)
Thursday 15 January 2026 14:00 - Orléans - Salle de Séminaires
Résumé :
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.
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