Lengths of saddle connections on random translation surfaces of large genus

Fuente: arXiv
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Main Authors: Masur, Howard, Rafi, Kasra, Randecker, Anja
Format: Preprint
Published: 2024
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author Masur, Howard
Rafi, Kasra
Randecker, Anja
author_facet Masur, Howard
Rafi, Kasra
Randecker, Anja
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2412_08727
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Lengths of saddle connections on random translation surfaces of large genus
Masur, Howard
Rafi, Kasra
Randecker, Anja
Geometric Topology
Probability
32G15 30F60 57M50
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.
title Lengths of saddle connections on random translation surfaces of large genus
topic Geometric Topology
Probability
32G15 30F60 57M50
url https://arxiv.org/abs/2412.08727