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In this paper, we investigate the asymptotic behavior of the non-simplesystole, which is the length of a shortest non-simple closed geodesic, on arandom closed hyperbolic surface on the moduli space $\mathcal{M}_g$ of Riemannsurfaces of genus $g$ endowed with the Weil-Petersson measure. We show that asthe genus $g$ goes to infinity, the non-simple systole of a generic hyperbolicsurface in $\mathcal{M}_g$ behaves exactly like $\log g$.

Non-simple systoles on random hyperbolic surfaces for large genus