{"paper":{"title":"Averages of determinants of Laplacians over moduli spaces for large genus","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.DG","math.SP"],"primary_cat":"math.GT","authors_text":"Yunhui Wu, Yuxin He","submitted_at":"2024-11-20T01:49:42Z","abstract_excerpt":"Let $\\mathcal{M}_g$ be the moduli space of hyperbolic surfaces of genus $g$ endowed with the Weil-Petersson metric. We view the regularized determinant $\\log \\det(\\Delta_{X})$ of Laplacian as a function on $\\mathcal{M}_g$ and show that there exists a universal constant $E>0$ such that as $g\\to \\infty$,\n  (1) the expected value of $\\left|\\frac{\\log \\det(\\Delta_{X})}{4\\pi(g-1)}-E \\right|$ over $\\mathcal{M}_g$ has rate of decay $g^{-\\delta}$ for some uniform constant $\\delta \\in (0,1)$;\n  (2) the expected value of $\\left|\\frac{\\log \\det(\\Delta_{X})}{4\\pi(g-1)}\\right|^\\beta$ over $\\mathcal{M}_g$ a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.12971","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/2411.12971/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"}