Non-simple systoles on random hyperbolic surfaces for large genus

2023/08/31 by Yuxin He, Yang Shen, He, Yuxin +5 · 1 citation
Mathematics · #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Geometry and complex manifolds #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.2308.16447

openalex publication_date 2023/08/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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 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 M_g behaves exactly like log g.

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