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

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.

arXiv comment76 pages, no figures

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Cited by in corpus (11)

• Masur-Veech volumes, frequencies of simple closed geodesics and intersection numbers of moduli spaces of curves
• Large genus asymptotic geometry of random square-tiled surfaces and of random multicurves
• Masur-Veech volumes and intersection theory: the principal strata of quadratic differentials
• Large genus asymptotics for lengths of separating closed geodesics on random surfaces
• An intersection-theoretic proof of the Harer-Zagier formula
• Uniform Lower Bound for Intersection Numbers of $\psi$-Classes
• Arbitrarily small spectral gaps for random hyperbolic surfaces with many cusps
• Masur--Veech volumes of quadratic differentials and their asymptotics
• On the large genus asymptotics of psi-class intersection numbers
• Les Houches lecture notes on moduli spaces of Riemann surfaces
• Around the combinatorial unit ball of measured foliations on bordered surfaces