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Growth of Weil-Petersson volumes and random hyperbolic surfaces of large genus (1012.2167v1)
Published 10 Dec 2010 in math.GN
Abstract: In this paper we study the asymptotic behavior of Weil-Petersson volumes of moduli spaces of hyperbolic surfaces of genus $g$ as $g \rightarrow \infty.$ We apply these asymptotic estimates to study the geometric properties of random hyperbolic surfaces, such as the Cheeger constant and the length of the shortest simple closed geodesic of a given combinatorial type.
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