Large genus asymptotics for intersection numbers and principal strata volumes of quadratic differentials

• 成果类型: Article
• 署名作者: Aggarwal, Amol
• 署名单位: Columbia University
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-021-01059-9
• 发表日期: 2021
• 页码: 897-1010
• 关键词: weil-petersson volumes; siegel-veech constants; MODULI SPACES; CLOSED GEODESICS; SURFACES; transformations; GROWTH

摘要

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.