{"paper":{"title":"Skewness tunes the small-drift record rate of random walks and L\\'{e}vy flights","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.MP","math.PR"],"primary_cat":"cond-mat.stat-mech","authors_text":"Jos\\'e Ricardo G. Mendon\\c{c}a","submitted_at":"2026-06-22T16:26:06Z","abstract_excerpt":"A random walk with small positive drift $\\mu$ sets new records at a rate $\\lambda(\\mu)$ that vanishes as $\\mu \\to 0$. For centered steps attracted to a stable law $Y$ with index $1 < \\alpha \\leq 2$ and positivity parameter $\\rho = P(Y>0)$, we find $\\lambda(\\mu) \\sim K\\mu^{(1-\\rho)/\\nu}$, $\\nu=1-1/\\alpha$, as $\\mu \\to 0$. The result is exact for Gaussian and strictly stable steps, and extends at the leading-power level to their domains of attraction. The exponent is set by the asymmetry only through $\\rho$, sweeping the interval $[1,\\,1/(\\alpha-1)]$ as the skewness varies. It recovers the Gauss"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.23553","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/2606.23553/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"}