A central limit theorem for prime geodesics on random surfaces of large genus

Sun-Kai Leung

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arXiv · 2608.17265

A central limit theorem for prime geodesics on random surfaces of large genus

Sun-Kai Leung

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Abstract

We show that, for Weil--Petersson random closed hyperbolic surfaces of large genus, the normalized weighted count of prime geodesics with norm in the interval $(X,X+H]$ is asymptotically Gaussian, provided $H \leq X$ and $H/\log X\to\infty$ as $X\to\infty$. In particular, it applies to intervals which are not necessarily short.

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Sun-Kai Leung. 2026-08-18. A central limit theorem for prime geodesics on random surfaces of large genus. https://arxiv.org/abs/2608.17265

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