Quantum Ergodicity for compact quotients of ${\rm SL}_d(\mathbb{R})/{\rm SO}(d)$ in the Benjamini-Schramm limit

Abstract

We study the limiting behavior of Maass forms on Benjamini-Schramm convergent sequences of compact quotients of ${\rm SL}_d(\mathbb{R})/{\rm SO}(d)$, $d\ge 3$, whose spectral parameter stays in a fixed window. We prove a form of Quantum Ergodicity in this level aspect which extends results of Le Masson and Sahlsten to the higher rank case.