{"paper":{"title":"Martin boundary of a reflected random walk on a half-space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Irina Ignatiouk-Robert","submitted_at":"2006-10-07T10:02:36Z","abstract_excerpt":"The complete representation of the Martin compactification for reflected random walks on a half-space $\\Z^d\\times\\N$ is obtained. It is shown that the full Martin compactification is in general not homeomorphic to the ``radial'' compactification obtained by Ney and Spitzer for the homogeneous random walks in $\\Z^d$ : convergence of a sequence of points $z_n\\in\\Z^{d-1}\\times\\N$ to a point of on the Martin boundary does not imply convergence of the sequence $z_n/|z_n|$ on the unit sphere $S^d$. Our approach relies on the large deviation properties of the scaled processes and uses Pascal's method"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0610242","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"}