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Lengths of saddle connections on random translation surfaces of large genus (2412.08727v1)
Published 11 Dec 2024 in math.GT and math.PR
Abstract: We determine the distribution of the number of saddle connections on a random translation surface of large genus. More specifically, for genus $g$ going 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 are independent.
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