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

Abstract

In this paper we study the asymptotic behavior of Weil-Petersson volumes of moduli spaces of hyperbolic surfaces of genus $g$ as $g\to \infty .$ 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.

References in corpus (5)

• An algebro-geometric proof of Witten's conjecture
• Combinatorial and algebro-geometric cohomology classes on the moduli spaces of curves
• Mirzakhani's recursion relations, Virasoro constraints and the KdV hierarchy
• On the large genus asymptotics of Weil-Petersson volumes
• Mirzakharni's recursion formula is equivalent to the Witten-Kontsevich theorem

Cited by in corpus (11)

• Random hyperbolic surfaces of large genus have first eigenvalues greater than $\frac{3}{16}-\epsilon$
• Short geodesic loops and $L^p$ norms of eigenfunctions on large genus random surfaces
• Random regular graphs and the systole of a random surface
• Moduli spaces of hyperbolic surfaces and their Weil-Petersson volumes
• Large genus asymptotic geometry of random square-tiled surfaces and of random multicurves
• Towards large genus asymtotics of intersection numbers on moduli spaces of curves
• Lectures and notes: Mirzakhani's volume recursion and approach for the Witten-Kontsevich theorem on moduli tautological intersection numbers
• Small eigenvalues of closed Riemann surfaces for large genus
• A new uniform lower bound on Weil-Petersson distance
• A Moebius inversion formula to discard tangled hyperbolic surfaces
• A remark on Mirzakhani's asymptotic formulae