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.

在本文中，我们在稳定曲线的模空间上分析了\(\psi \) -类（也称为相关器）之间的交集数的大属渐近性。我们的证明通过对唯一确定这些相关器的递归关系（Virasoro 约束）进行组合分析，同时将这些关系中的系数与某个非对称简单随机游走的跳跃概率进行比较。作为该结果的应用，我们提供了与二次微分模空间中的主要地层相关的 Masur-Veech 体积和面积 Siegel-Veech 常数的大属极限。这些证实了 Delecroix-Goujard-Zograf-Zorich 对 2019 年的预测。