{"paper":{"title":"Martin boundary of a killed random walk on a quadrant","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Christophe Loree, Irina Ignatiouk-Robert","submitted_at":"2009-02-28T12:16:06Z","abstract_excerpt":"A complete representation of the Martin boundary of killed random walks on the quadrant ${\\mathbb{N}}^*\\times{\\mathbb{N}}^*$ is obtained. It is proved that the corresponding full Martin compactification of the quadrant ${\\mathbb{N}}^*\\times{\\mathbb{N}}^*$ is homeomorphic to the closure of the set $\\{w={z}/{(1+|z|)}:z\\in{\\mathbb{N}}^*\\times{\\mathbb{N}}^*\\}$ in ${\\mathbb{R}}^2$. The method is based on a ratio limit theorem for local processes and large deviation techniques."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0903.0070","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"}