{"paper":{"title":"The Slow Bond Random Walk and the Snapping Out Brownian Motion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Diogo S. da Silva, Dirk Erhard, Tertuliano Franco","submitted_at":"2019-05-20T13:17:34Z","abstract_excerpt":"We consider the continuous time symmetric random walk with a slow bond on $\\mathbb Z$, which rates are equal to $1/2$ for all bonds, except for the bond of vertices $\\{-1,0\\}$, which associated rate is given by $\\alpha n^{-\\beta}/2$, where $\\alpha\\geq 0$ and $\\beta\\in [0,\\infty]$ are the parameters of the model. We prove here a functional central limit theorem for the random walk with a slow bond: if $\\beta<1$, then it converges to the usual Brownian motion. If $\\beta\\in (1,\\infty]$, then it converges to the reflected Brownian motion. And at the critical value $\\beta=1$, it converges to the sn"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.08084","kind":"arxiv","version":1},"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"}