{"paper":{"title":"Asymptotics of one-dimensional forest fire processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Nicolas Fournier, Xavier Bressaud","submitted_at":"2008-12-05T09:34:24Z","abstract_excerpt":"We consider the so-called one-dimensional forest fire process. At each site of $\\mathbb{Z}$, a tree appears at rate $1$. At each site of $\\mathbb{Z}$, a fire starts at rate ${\\lambda}>0$, immediately destroying the whole corresponding connected component of trees. We show that when ${\\lambda}$ is made to tend to $0$ with an appropriate normalization, the forest fire process tends to a uniquely defined process, the dynamics of which we precisely describe. The normalization consists of accelerating time by a factor $\\log(1/{\\lambda})$ and of compressing space by a factor ${\\lambda}\\log(1/{\\lambd"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0812.1099","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"}