{"paper":{"title":"Alpha-stable random walk has massive thorns","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Alexander Bendikov, Wojciech Cygan","submitted_at":"2013-07-18T14:04:26Z","abstract_excerpt":"We introduce and study a class of random walks defined on the integer lattice $ \\mathbb{Z} ^d$ -- a discrete space and time counterpart of the symmetric $\\alpha$-stable process in $\\mathbb{R} ^d$. When $0< \\alpha <2$ any coordinate axis in $\\mathbb{Z} ^d$, $d\\geq 3$, is a non-massive set whereas any cone is massive. We provide a necessary and sufficient condition for the thorn to be a massive set."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.4947","kind":"arxiv","version":3},"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"}