Typical hyperbolic surfaces have a spectral gap greater than $2/9 - ε$
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866918439430389760 |
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| author | Anantharaman, Nalini Monk, Laura |
| author_facet | Anantharaman, Nalini Monk, Laura |
| contents | In this article, we prove that typical hyperbolic surfaces, sampled with the Weil-Petersson probability measure, have a spectral gap at least $2/9 - ε$. This is an intermediate result on the way to our proof of the optimal spectral gap $1/4 - ε$, building on the results of the first part of this series. A significant part of the proof is an explicit inclusion-exclusion argument to exclude tangles at the level of precision $1/g$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_09792 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Typical hyperbolic surfaces have a spectral gap greater than $2/9 - ε$ Anantharaman, Nalini Monk, Laura Spectral Theory Primary 58J50, 32G15, Secondary 05C80, 11F72 In this article, we prove that typical hyperbolic surfaces, sampled with the Weil-Petersson probability measure, have a spectral gap at least $2/9 - ε$. This is an intermediate result on the way to our proof of the optimal spectral gap $1/4 - ε$, building on the results of the first part of this series. A significant part of the proof is an explicit inclusion-exclusion argument to exclude tangles at the level of precision $1/g$. |
| title | Typical hyperbolic surfaces have a spectral gap greater than $2/9 - ε$ |
| topic | Spectral Theory Primary 58J50, 32G15, Secondary 05C80, 11F72 |
| url | https://arxiv.org/abs/2604.09792 |