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arXiv · 2603.15233

On uniform large genus asymptotics of Witten's intersection numbers

Jindong Guo·Di Yang·Don Zagier
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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.

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Jindong Guo, Di Yang, Don Zagier. 2026-03-16. On uniform large genus asymptotics of Witten's intersection numbers. https://arxiv.org/abs/2603.15233

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