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

TL;DR

This paper extends quantum ergodicity results to higher rank symmetric spaces, analyzing the behavior of Maass forms on sequences of compact quotients of ${ m SL}_d( eals)/{ m SO}(d)$ in the Benjamini-Schramm limit.

Contribution

It generalizes quantum ergodicity to higher rank symmetric spaces for sequences of compact quotients with spectral parameters in a fixed window.

Findings

Proves quantum ergodicity in the higher rank case.

Extends results of Le Masson and Sahlsten.

Analyzes Maass forms on Benjamini-Schramm convergent sequences.

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.