Spectral gap with polynomial rate for random covering surfaces
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915286383329280 |
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| author | Hide, Will Macera, Davide Thomas, Joe |
| author_facet | Hide, Will Macera, Davide Thomas, Joe |
| contents | In this note we show that the recent work of Magee, Puder and van Handel [MPvH25] can be applied to obtain an optimal spectral gap result with polynomial error rate for uniformly random covers of closed hyperbolic surfaces. Let $X$ be a closed hyperbolic surface. We show there exists $b,c>0$ such that a uniformly random degree-$n$ cover $X_{n}$ of $X$ has no new Laplacian eigenvalues below $\frac{1}{4}-cn^{-b}$ with probability tending to $1$ as $n\to\infty$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_08479 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Spectral gap with polynomial rate for random covering surfaces Hide, Will Macera, Davide Thomas, Joe Spectral Theory Differential Geometry Operator Algebras Probability 58J50 In this note we show that the recent work of Magee, Puder and van Handel [MPvH25] can be applied to obtain an optimal spectral gap result with polynomial error rate for uniformly random covers of closed hyperbolic surfaces. Let $X$ be a closed hyperbolic surface. We show there exists $b,c>0$ such that a uniformly random degree-$n$ cover $X_{n}$ of $X$ has no new Laplacian eigenvalues below $\frac{1}{4}-cn^{-b}$ with probability tending to $1$ as $n\to\infty$. |
| title | Spectral gap with polynomial rate for random covering surfaces |
| topic | Spectral Theory Differential Geometry Operator Algebras Probability 58J50 |
| url | https://arxiv.org/abs/2505.08479 |