Journal
INVENTIONES MATHEMATICAE
Volume 226, Issue 3, Pages 897-1010Publisher
SPRINGER HEIDELBERG
DOI: 10.1007/s00222-021-01059-9
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Funding
- NSF [NSF DMS-1664619, DGE-1144152]
- Harvard Merit/Graduate Society Term-time Research Fellowship
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This paper analyzes the large genus asymptotics for intersection numbers between psi-classes on the moduli space of stable curves through a combinatorial analysis of the recursive relations and comparison with jump probabilities of a certain random walk. The results provide large genus limits for Masur-Veech volumes and area Siegel-Veech constants associated with principal strata in the moduli space of quadratic differentials, confirming predictions from 2019.
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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