In this paper we consider the large genus asymptotics for Masur-Veech volumes of arbitrary strata of Abelian differentials. Through a combinatorial analysis of an algorithm proposed in 2002 by Eskin-Okounkov to exactly evaluate these quantities, we show that the volume $\nu_1 \big( \mathcal{H}_1 (m) \big)$ of a stratum indexed by a partition $m = (m_1, m_2, \ldots , m_n)$ is $\big( 4 + o(1) \big) \prod_{i = 1}^n (m_i + 1)^{-1}$ as $2g - 2 = \sum_{i = 1}^n m_i$ tends to $\infty$. This confirms a prediction of Eskin-Zorich and generalizes some of the recent results of Chen-Moeller-Zagier and Sauvaget, who established these limiting statements in the special cases $m = 1^{2g - 2}$ and $m = (2g - 2)$, respectively. We also include an Appendix by Anton Zorich that uses our main result to deduce the large genus asymptotics for Siegel-Veech constants that count certain types of saddle connections.

中文翻译：

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阿贝尔微分地层体积的大属渐近

在本文中，我们考虑了阿贝尔微分的任意层​​的 Masur-Veech 体积的大属渐近性。通过对 Eskin-Okounkov 于 2002 年提出的算法的组合分析来精确评估这些数量，我们表明，由 a 索引的层的体积 $\nu_1 \big( \mathcal{H}_1 (m) \big)$分区 $m = (m_1, m_2, \ldots , m_n)$ 是 $\big( 4 + o(1) \big) \prod_{i = 1}^n (m_i + 1)^{-1}$ 作为$2g - 2 = \sum_{i = 1}^n m_i$ 趋向于 $\infty$。这证实了 Eskin-Zorich 的预测，并概括了 Chen-Moeller-Zagier 和 Sauvaget 最近的一些结果，他们在特殊情况下建立了这些限制性陈述 $m = 1^{2g - 2}$ 和 $m = (2g - 2)$，分别。