Abstract
In this paper, we investigate the geometric properties of random hyperbolic surfaces of large genus. We describe the relationship between the behavior of lengths of simple closed geodesics on a hyperbolic surface and properties of the moduli space of such surfaces. First, we study the asymptotic behavior of Weil-Petersson volume $V^{g,n}$ of the moduli spaces of hyperbolic surfaces of genus $g$ with $n$ punctures as $g \to \infty$. Then we discuss basic geometric properties of a random hyperbolic surface of genus $g$ with respect to the Weil-Petersson measure as $g \to \infty$.
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