3 papers
math.DG2026
Uniform spectral gaps for random hyperbolic surfaces with not many cusps
Yuxin He, Yunhui Wu, Yuhao Xue
In this paper, we investigate uniform spectral gaps for Weil-Petersson random hyperbolic surfaces with not many cusps. We show that if where $α\in \left[0,\frac{1}{2}\…
math.GT2025
The Brownian loop measure on Riemann surfaces and applications to length spectra
Yilin Wang, Yuhao Xue
We prove a simple identity relating the length spectrum of a Riemann surface to that of the same surface with an arbitrary number of additional cusps. Our proof uses the Brownian l…
math.GT2025
Non-simple systoles on random hyperbolic surfaces for large genus
Yuxin He, Yang Shen, Yunhui Wu +1
In this paper, we investigate the asymptotic behavior of the non-simple systole, which is the length of a shortest non-simple closed geodesic, on a random closed hyperbolic surface…