Critical Exponents on Hyperbolic Surfaces with Long Boundaries and the Asymptotic Weil-Petersson Form
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866929676541231104 |
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| author | Talbott, Henry |
| author_facet | Talbott, Henry |
| contents | We study the critical exponent random variable $δ_X$ on moduli spaces of hyperbolic surfaces with boundary, using the normalized Weil-Petersson measures $dμ_{WP}$ as probability measures. We use the spine graph construction of Bowditch and Epstein to compare this random variable to the corresponding critical exponent random variable $δ_Γ$ on moduli spaces of metric ribbon graphs with the normalized Kontsevich measures $dμ_K$, proving an asymptotic convergence-in-mean result in the long boundary length regime. In particular, we show that $dμ_K$ approximately pulls back to $dμ_{WP}$ with quantitative uniform estimates. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_08447 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Critical Exponents on Hyperbolic Surfaces with Long Boundaries and the Asymptotic Weil-Petersson Form Talbott, Henry Geometric Topology Probability We study the critical exponent random variable $δ_X$ on moduli spaces of hyperbolic surfaces with boundary, using the normalized Weil-Petersson measures $dμ_{WP}$ as probability measures. We use the spine graph construction of Bowditch and Epstein to compare this random variable to the corresponding critical exponent random variable $δ_Γ$ on moduli spaces of metric ribbon graphs with the normalized Kontsevich measures $dμ_K$, proving an asymptotic convergence-in-mean result in the long boundary length regime. In particular, we show that $dμ_K$ approximately pulls back to $dμ_{WP}$ with quantitative uniform estimates. |
| title | Critical Exponents on Hyperbolic Surfaces with Long Boundaries and the Asymptotic Weil-Petersson Form |
| topic | Geometric Topology Probability |
| url | https://arxiv.org/abs/2501.08447 |