{"paper":{"title":"Long-range correlations with finite-size effects from a superposition of uncorrelated pulses with power-law distributed durations","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"M. A. Korzeniowska, O. E. Garcia","submitted_at":"2024-10-08T11:35:14Z","abstract_excerpt":"Long-range correlations manifested as power spectral density scaling $1/f^\\beta$ for frequency $f$ and a range of exponents $\\beta$ are investigated for a superposition of uncorrelated pulses with distributed durations $\\tau$. Closed-form expressions for the frequency power spectral density are derived for a one-sided exponential pulse function and several variants of bounded and unbounded power-law distributions of pulse durations ${P_\\tau(\\tau)\\sim1/\\tau^\\alpha}$ with abrupt and smooth cutoffs. The asymptotic scaling relation $\\beta=3-\\alpha$ is demonstrated for $1<\\alpha<3$ in the limit of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.07249","kind":"arxiv","version":4},"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/2410.07249/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"}