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arXiv · 2004.05042

Large Genus Asymptotics for Intersection Numbers and Principal Strata Volumes of Quadratic Differentials

Amol Aggarwal
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Abstract

In this paper we analyze the large genus asymptotics for intersection numbers between $\psi$-classes, also called correlators, on the moduli space of stable curves. Our proofs proceed through a combinatorial analysis of the recursive relations (Virasoro constraints) that uniquely determine these correlators, together with a comparison between the coefficients in these relations with the jump probabilities of a certain asymmetric simple random walk. As an application of this result, we provide the large genus limits for Masur-Veech volumes and area Siegel-Veech constants associated with principal strata in the moduli space of quadratic differentials. These confirm predictions of Delecroix-Goujard-Zograf-Zorich from 2019.

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BibTeXRIS

Amol Aggarwal. 2020-04-10. Large Genus Asymptotics for Intersection Numbers and Principal Strata Volumes of Quadratic Differentials. https://doi.org/10.1007/s00222-021-01059-9

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