Critical exponents on hyperbolic surfaces with long boundaries and the asymptotic Weil-Petersson form
Abstract
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.
Fields of Study & Subjects
Geometric Analysis and Curvature Flows
advanced mathematical theories
Advanced Mathematical Modeling in Engineering
Publication details
- Journal / source
- Advances in Mathematics
- Volume
- 500
- Pages
- 111061–111061
- Publication date
- 2 June 2026
- Language
- EN