Growth of Weil-Petersson volumes and random hyperbolic surfaces of large genus

Details Growth of Weil-Petersson volumes and random hyperbolic surfaces of large genus Growth of Weil-Petersson volumes and random hyperbolic surfaces of large genus

2010-12-10

arxiv.org/abs/1012.2167v1

Mathematics

General Topology

Scientific paper

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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