{"paper":{"title":"All You Need is not $\\Omega_\\mathrm{gw}$: Beyond the Mean of the Cross-Correlation Estimator when Searching for an Astrophysical Gravitational-Wave Background","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["astro-ph.HE","astro-ph.IM"],"primary_cat":"gr-qc","authors_text":"Emanuele Berti, Francesco Iacovelli, Haowen Zhong, Vuk Mandic","submitted_at":"2026-08-11T16:26:47Z","abstract_excerpt":"Searches for the stochastic gravitational-wave background (SGWB) using ground-based detectors rely heavily on the cross-correlation estimator $\\bar C_f$, whose statistical properties determine the theoretical foundation for inference frameworks built on it. Past analyses usually assume Gaussianity of $\\bar C_f$, but this assumption has not been systematically tested for a background of astrophysical origin like the one produced by compact binary coalescences. In this work, we decompose $\\bar C_f$ into three physically motivated components: (1) the mean intensity, (2) the geometrical shot noise"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.11119","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/2608.11119/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"}