August 2023
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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 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 behaves exactly like .