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QUANTUM ERGODICITY FOR COMPACT QUOTIENTS OF $\operatorname {SL}_d({\mathbb R})/\textrm {SO}(d)$ IN THE BENJAMINI–SCHRAMM LIMIT

Part of: Discontinuous groups and automorphic forms Partial differential equations on manifolds; differential operators

Published online by Cambridge University Press:  13 December 2021

Farrell Brumley  and
Jasmin Matz Open the ORCID record for Jasmin Matz [Opens in a new window]
Farrell Brumley
Affiliation:
Université Sorbonne Paris Nord, Laga – Institut Galilée, 99 Avenue Jean Baptiste Clément, Villetaneuse 93430, France (brumley@math.univ-paris13.fr)
Jasmin Matz*
Affiliation:
Department of Mathematical Science, University of Copenhagen, Universitetsparken 5, Copenhagen 2100, Denmark
*
matz@math.ku.dk
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Abstract

We study the limiting behavior of Maass forms on sequences of large-volume compact quotients of $\operatorname {SL}_d({\mathbb R})/\textrm {SO}(d)$, $d\ge 3$, 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.

Keywords

quantum ergodicityBenjamini–Schramm convergencelocally symmetric spaces

MSC classification

Primary: 58J51: Relations between spectral theory and ergodic theory, e.g. quantum unique ergodicity
Secondary: 11F72: Spectral theory; Selberg trace formula
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 22 , Issue 5 , September 2023 , pp. 2075 - 2115
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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