{"paper":{"title":"Kurtosis and Large--Scale Structure","license":"","headline":"","cross_cats":[],"primary_cat":"astro-ph","authors_text":"Lauro Moscardini, Paolo Catelan","submitted_at":"1993-08-04T11:04:43Z","abstract_excerpt":"We discuss the non--linear growth of the excess kurtosis parameter of the smoothed density fluctuation field $\\delta$, $S_4\\equiv[\\lan\\delta^{\\,4}\\ran-3\\lan\\delta^{\\,2}\\ran^2]/ \\lan\\delta^{\\,2}\\ran^3$ in an Einstein--de Sitter universe. We assume Gaussian primordial density fluctuations with scale--free power spectrum $P(k)\\propto k^{\\,n}$ and analyze the dependence of $S_4$ on primordial spectral index $n$, after smoothing with a Gaussian filter. As already known for the skewness ratio $S_3$, the kurtosis parameter is a {\\it decreasing function} of $n$, both in exact perturbative theory and i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"astro-ph/9308002","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/astro-ph/9308002/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"}