{"paper":{"title":"The frog model with death and drift on free products of complete graphs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"\\'Elcio Lebensztayn, Jaime Utria, Nancy Garcia","submitted_at":"2026-06-08T20:48:42Z","abstract_excerpt":"We study the frog model with death and drift on $\\mathbb{D}_{m,d}$, the free product of $d+1$ copies of the complete graph of order $m$. Active and inactive particles are located at the vertices of $\\mathbb{D}_{m,d}$. Each active particle performs a $\\alpha$-biased random walk towards the root of $\\mathbb{D}_{m,d}$, dying after a random lifetime with a geometric distribution of parameter $1-p$. Each inactive particle remains dormant until an active particle visits its location. We present conditions on the parameters $\\alpha$ and $p$ for the process to die out almost surely and to survive with"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.10165","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/2606.10165/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"}