Towards large genus asymtotics of intersection numbers on moduli spaces of curves

Abstract

We explicitly compute the diverging factor in the large genus asymptotics of the Weil-Petersson volumes of the moduli spaces of $n$-pointed complex algebraic curves. Modulo a universal multiplicative constant we prove the existence of a complete asymptotic expansion of the Weil-Petersson volumes in the inverse powers of the genus with coefficients that are polynomials in $n$. This is done by analyzing various recursions for the more general intersection numbers of tautological classes, whose large genus asymptotic behavior is also extensively studied.

References in corpus (5)

• An algebro-geometric proof of Witten's conjecture
• Mirzakhani's recursion relations, Virasoro constraints and the KdV hierarchy
• On the large genus asymptotics of Weil-Petersson volumes
• Growth of Weil-Petersson volumes and random hyperbolic surfaces of large genus
• Mirzakharni's recursion formula is equivalent to the Witten-Kontsevich theorem

Cited by in corpus (4)

• JT gravity as a matrix integral
• Geometric Microstates for the Three Dimensional Black Hole?
• Large genus asymptotic geometry of random square-tiled surfaces and of random multicurves
• JT gravity and the asymptotic Weil-Petersson volume