{"paper":{"title":"Activated Random Walk on a cycle","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","math-ph","math.CO","math.MP"],"primary_cat":"math.PR","authors_text":"Christopher Hoffman, Jacob Richey, Riddhipratim Basu, Shirshendu Ganguly","submitted_at":"2017-09-26T17:58:51Z","abstract_excerpt":"We consider Activated Random Walk (ARW), a particle system with mass conservation, on the cycle $\\mathbb{Z}/n\\mathbb{Z}$. One starts with a mass density $\\mu>0$ of initially active particles, each of which performs a simple symmetric random walk at rate one and falls asleep at rate $\\lambda>0.$ Sleepy particles become active on coming in contact with other active particles. There have been several recent results concerning fixation/non-fixation of the ARW dynamics on infinite systems depending on the parameters $\\mu$ and $\\lambda$. On the finite graph $\\mathbb{Z}/n\\mathbb{Z}$, unless there are"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.09163","kind":"arxiv","version":2},"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"}