Arbitrarily small spectral gaps for random hyperbolic surfaces with many cusps
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866915392351371264 |
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| author | Shen, Yang Wu, Yunhui |
| author_facet | Shen, Yang Wu, Yunhui |
| contents | Let $\mathcal{M}_{g,n(g)}$ be the moduli space of hyperbolic surfaces of genus $g$ with $n(g)$ punctures endowed with the Weil-Petersson metric. In this paper we study the asymptotic behavior of the Cheeger constants and spectral gaps of random hyperbolic surfaces in $\mathcal{M}_{g,n(g)}$, when $n(g)$ grows slower than $g$ as $g\to \infty$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2203_15681 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Arbitrarily small spectral gaps for random hyperbolic surfaces with many cusps Shen, Yang Wu, Yunhui Differential Geometry Geometric Topology Probability Spectral Theory Let $\mathcal{M}_{g,n(g)}$ be the moduli space of hyperbolic surfaces of genus $g$ with $n(g)$ punctures endowed with the Weil-Petersson metric. In this paper we study the asymptotic behavior of the Cheeger constants and spectral gaps of random hyperbolic surfaces in $\mathcal{M}_{g,n(g)}$, when $n(g)$ grows slower than $g$ as $g\to \infty$. |
| title | Arbitrarily small spectral gaps for random hyperbolic surfaces with many cusps |
| topic | Differential Geometry Geometric Topology Probability Spectral Theory |
| url | https://arxiv.org/abs/2203.15681 |