On the large genus asymptotics of psi-class intersection numbers

TL;DR

This paper provides a new proof for the large genus asymptotic behavior of psi-class intersection numbers using explicit generating series formulas, and explores polynomiality phenomena in high genera.

Contribution

It introduces a novel proof of a conjecture on large genus asymptotics and investigates polynomiality in psi-class intersection numbers.

Findings

Confirmed the conjecture on large genus asymptotics

Derived explicit formulas for generating series

Identified polynomiality phenomena in high genera

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.