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

Sun-Kai Leung

math.NTarXiv:2608.17265

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 ≤ X and H/ X∞ as X∞. In particular, it applies to intervals which are not necessarily short.

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