Estimates of Weil-Petersson volumes via effective divisors

Abstract

We study the asymptotics of the Weil-Petersson volumes of the moduli spaces of compact Riemann surfaces of genus $g$ with $n$ punctures, for fixed $n$ as $g\to \infty$.

References in corpus (3)

• Weil-Petersson volumes of moduli spaces of curves and the genus expansion in two dimensional gravity
• Invertible Cohomological Field Theories and Weil-Petersson volumes
• Explicit upper bound for the Weil-Petersson volumes

Cited by in corpus (13)

• On the large genus asymptotics of Weil-Petersson volumes
• Growth of the Weil-Petersson Diameter of Moduli Space
• Large genus asymptotics for lengths of separating closed geodesics on random surfaces
• Growth of the Weil-Petersson inradius of moduli space
• Triangulated Surfaces in Twistor Space: A Kinematical Set up for Open/Closed String Duality
• Lectures and notes: Mirzakhani's volume recursion and approach for the Witten-Kontsevich theorem on moduli tautological intersection numbers
• Recursion formulae of higher Weil-Petersson volumes
• Arbitrarily small spectral gaps for random hyperbolic surfaces with many cusps
• The degree of the Jacobian locus and the Schottky problem
• Asymptotic properties of the set of systoles of arithmetic Riemann surfaces
• On the Weil-Petersson curvature of the moduli space of Riemann surfaces of large genus
• The factorial growth of topological recursion
• Estimates for the average scalar curvature of the Weil-Petersson metric on the Moduli space ${\overline{\mathcal{M}}}_g$