{"paper":{"title":"The Frog Model on $\\mathbb Z$ with Random Discrete Weibull Lifetimes and Biased Nearest-Neighbour Random Walks","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Prates Machado Fabio, Ram\\'irez-Gonz\\'alez J.H.","submitted_at":"2026-06-09T16:30:27Z","abstract_excerpt":"We study the frog model on $\\mathbb Z$ with particle-wise random discrete Weibull lifetimes and biased nearest-neighbour random walks. Each particle has an independent survival parameter $\\pi\\in(0,1)$. Conditionally on $\\pi=p$, its lifetime $\\Xi$ satisfies $$\n  \\mathbb P(\\Xi\\ge k\\mid \\pi=p)=p^{k^\\gamma},\n  \\, k\\in\\mathbb{N}_0, $$ where $\\gamma>0$. The distribution of $\\pi$ is assumed to have right-edge density $$\n  f_\\pi(u)\\sim (1-u)^{\\beta-1}\n  L\\left(\\frac1{1-u}\\right),\n  \\, u\\uparrow1, $$ where $\\beta>0$ and $L:(0,\\infty)\\to(0,\\infty)$ is a slowly varying function at infinity. The main step"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.11068","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/2606.11068/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"}