On uniform large genus asymptotics of Witten's intersection numbers

TL;DR

This paper derives uniform large genus asymptotics for primitive psi-class intersection numbers on moduli spaces, extends the results to include zeros, and applies the findings to Painlevé I solutions, also providing a new proof of polynomiality conjecture.

Contribution

It introduces a uniform asymptotic analysis for psi-class intersection numbers, extending previous results and applying a novel proof technique to the polynomiality conjecture.

Findings

Established uniform large genus asymptotics for primitive psi-class intersection numbers

Extended asymptotics to include insertions of zeros

Provided a new proof of the polynomiality conjecture

Abstract

Following ideas from [14], we give a uniform large genus asymptotics for primitive psi-class intersection numbers on the moduli space of stable algebraic curves, and extend this result including insertions of zeros in a certain uniform way. Application to a particular formal solution of the Painlev\'e I equation is given. We also use a method from [14] to give a new proof of the polynomiality conjecture on large genus asymptotic expansions of psi-class intersection numbers.