Non-simple systoles on random hyperbolic surfaces for large genus

Fuente: arXiv
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Autores principales: He, Yuxin, Shen, Yang, Wu, Yunhui, Xue, Yuhao
Formato: Preprint
Publicado: 2023
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author He, Yuxin
Shen, Yang
Wu, Yunhui
Xue, Yuhao
author_facet He, Yuxin
Shen, Yang
Wu, Yunhui
Xue, Yuhao
contents In this paper, we investigate the asymptotic behavior of the non-simple systole, which is the length of a shortest non-simple closed geodesic, on a random closed hyperbolic surface on the moduli space $\mathcal{M}_g$ of Riemann surfaces of genus $g$ endowed with the Weil-Petersson measure. We show that as the genus $g$ goes to infinity, the non-simple systole of a generic hyperbolic surface in $\mathcal{M}_g$ behaves exactly like $\log g$.
format Preprint
id arxiv_https___arxiv_org_abs_2308_16447
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Non-simple systoles on random hyperbolic surfaces for large genus
He, Yuxin
Shen, Yang
Wu, Yunhui
Xue, Yuhao
Geometric Topology
Complex Variables
Differential Geometry
Probability
In this paper, we investigate the asymptotic behavior of the non-simple systole, which is the length of a shortest non-simple closed geodesic, on a random closed hyperbolic surface on the moduli space $\mathcal{M}_g$ of Riemann surfaces of genus $g$ endowed with the Weil-Petersson measure. We show that as the genus $g$ goes to infinity, the non-simple systole of a generic hyperbolic surface in $\mathcal{M}_g$ behaves exactly like $\log g$.
title Non-simple systoles on random hyperbolic surfaces for large genus
topic Geometric Topology
Complex Variables
Differential Geometry
Probability
url https://arxiv.org/abs/2308.16447