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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…
math.GT2024
Prime geodesic theorem and closed geodesics for large genus
Yunhui Wu, Yuhao Xue
Let be the moduli space of hyperbolic surfaces of genus endowed with the Weil-Petersson metric. In this paper, we show that for any , as , fo…