On the large genus asymptotics of psi-class intersection numbers

Abstract

Based on an explicit formula of the generating series for the $n$-point psi-class intersection numbers (cf. Bertola et. al. [4]), we give a novel proof of a conjecture of Delecroix et. al. [9] regarding the large genus uniform leading asymptotics of the psi-class intersection numbers. We also investigate polynomiality phenomenon in the large genera.

Corrected a mistake in Lemma 8; added the proof of the identity (54); added a few more details. 35 pages

References in corpus (7)

• Gromov-Witten theory, Hurwitz numbers, and Matrix models, I
• An algebro-geometric proof of Witten's conjecture
• Correlation functions of the KdV hierarchy and applications to intersection numbers over ${\overline{\mathcal{M}}}_{g,n}$
• Emergent Geometry and Mirror Symmetry of A Point
• Large Genus Asymptotics for Intersection Numbers and Principal Strata Volumes of Quadratic Differentials
• Simple Lie algebras, Drinfeld--Sokolov hierarchies, and multi-point correlation functions
• Uniform Lower Bound for Intersection Numbers of $\psi$-Classes

Cited by in corpus (1)

• Higher genus meanders and Masur-Veech volumes