{"paper":{"title":"Large Genus Asymptotics for Siegel-Veech Constants","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.DS"],"primary_cat":"math.GT","authors_text":"Amol Aggarwal","submitted_at":"2018-10-11T19:58:39Z","abstract_excerpt":"In this paper we consider the large genus asymptotics for two classes of Siegel-Veech constants associated with an arbitrary connected stratum $\\mathcal{H} (\\alpha)$ of Abelian differentials. The first is the saddle connection Siegel-Veech constant $c_{\\text{sc}}^{m_i, m_j} \\big( \\mathcal{H} (\\alpha) \\big)$ counting saddle connections between two distinct, fixed zeros of prescribed orders $m_i$ and $m_j$, and the second is the area Siegel-Veech constant $c_{\\text{area}} \\big( \\mathcal{H}(\\alpha) \\big)$ counting maximal cylinders weighted by area. By combining a combinatorial analysis of explic"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.05227","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1810.05227/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}