{"paper":{"title":"Local Weyl law and length-minimising loops on hyperbolic surfaces","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":["math.GT","math.MP","math.SP"],"primary_cat":"math-ph","authors_text":"Daniel Meriaz","submitted_at":"2026-07-27T07:01:38Z","abstract_excerpt":"We study the variance of a local Weyl law over a fixed smooth energy window, when averaged over large Weil--Petersson hyperbolic surfaces. Our results are consistent with the predictions of Berry's random wave model. Our approach allows to explicitly integrate certain test functions which depend on lengths of based geodesic loops, and relate them to the associated lengths of the closed geodesics in their free-homotopy class. We thus utilise the work of Mirzakhani, with exact stationary phase arguments, to identify correct main and error terms, making explicit the asymptotic behaviour of the va"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.24060","kind":"arxiv","version":1},"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/2607.24060/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"}