Quantum ergodicity in the Benjamini--Schramm limit for locally symmetric spaces
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866917377923350528 |
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| author | Brumley, Farrell Marshall, Simon Matz, Jasmin Peterson, Carsten |
| author_facet | Brumley, Farrell Marshall, Simon Matz, Jasmin Peterson, Carsten |
| contents | We prove that for almost all symmetric spaces $X$ and for any sequence of compact locally symmetric spaces $Y_n$ which is uniformly discrete, has a uniform spectral gap, and converges in the sense of Benjamini--Schramm to $X$, the joint eigenfunctions of all invariant differential operators on $Y_n$ delocalize on average when their spectral parameters are taken to lie in a fixed spectral window. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_01075 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Quantum ergodicity in the Benjamini--Schramm limit for locally symmetric spaces Brumley, Farrell Marshall, Simon Matz, Jasmin Peterson, Carsten Spectral Theory Mathematical Physics Number Theory Representation Theory 58J51, 11F72, 37D40, 43A90, 53C35 We prove that for almost all symmetric spaces $X$ and for any sequence of compact locally symmetric spaces $Y_n$ which is uniformly discrete, has a uniform spectral gap, and converges in the sense of Benjamini--Schramm to $X$, the joint eigenfunctions of all invariant differential operators on $Y_n$ delocalize on average when their spectral parameters are taken to lie in a fixed spectral window. |
| title | Quantum ergodicity in the Benjamini--Schramm limit for locally symmetric spaces |
| topic | Spectral Theory Mathematical Physics Number Theory Representation Theory 58J51, 11F72, 37D40, 43A90, 53C35 |
| url | https://arxiv.org/abs/2604.01075 |