{"paper":{"title":"Bounds of memory strength for power-law series","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.soc-ph"],"primary_cat":"physics.data-an","authors_text":"Dan Yang, Fangjian Guo, Tao Zhou, Zhi-Dan Zhao, Zimo Yang","submitted_at":"2015-06-30T14:04:40Z","abstract_excerpt":"Many time series produced by complex systems are empirically found to follow power-law distributions with different exponents $\\alpha$. By permuting the independently drawn samples from a power-law distribution, we present non-trivial bounds on the memory strength (1st-order autocorrelation) as a function of $\\alpha$, which are markedly different from the ordinary $\\pm 1$ bounds for Gaussian or uniform distributions. When $1 < \\alpha \\leq 3$, as $\\alpha$ grows bigger, the upper bound increases from 0 to +1 while the lower bound remains 0; when $\\alpha > 3$, the upper bound remains +1 while the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.09096","kind":"arxiv","version":6},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"}