Year: 2026
Type: preprint
Abstract: In this paper, we investigate uniform spectral gaps for Weil-Petersson random hyperbolic surfaces with not many cusps. We show that if $n=O(g^α)$ where $α\in \left[0,\frac{1}{2}\right)$, then for any $ε>0$, a random cusped hyperbolic surface in $\mathcal{M}_{g,n}$ has no eigenvalues in $\left(0,\frac{1}{4}-\left(\frac{1}{6(1-α)}\right)^2-ε\right)$. If $α$ is close to $\frac{1}{2}$, this gives a new uniform lower bound $\frac{5}{36}-ε$ for the spectral gaps of Weil-Petersson random hyperbolic surfaces. The major contribution of this work is to reveal a critical phenomenon of ``second order cancellation".
Source: arXiv (Cornell University)
Authors: He, Yuxin, Wu, Yunhui, Xue, Yuhao
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: G2027560089, G6390231956
OpenAlex ID: W7128517735
Cites:
Cited by:
Related to: