Lengths of saddle connections on random translation surfaces of large genus

Howard Masur; Kasra Rafi; Anja Randecker

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arXiv · 2412.08727

Lengths of saddle connections on random translation surfaces of large genus

Howard Masur·Kasra Rafi·Anja Randecker

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Abstract

We determine the distribution of the number of saddle connections on a random translation surface of large genus. More specifically, for genus $g$ tending to infinity, the number of saddle connections with lengths in a given interval $[\frac{a}{g}, \frac{b}{g}]$ converges in distribution to a Poisson distributed random variable. Furthermore, the numbers of saddle connections associated to disjoint intervals of lengths are independent.

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Howard Masur, Kasra Rafi, Anja Randecker. 2024-12-11. Lengths of saddle connections on random translation surfaces of large genus. https://arxiv.org/abs/2412.08727

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