{"paper":{"title":"Weak convergence of random walks conditioned to stay away","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Domokos Sz\\'asz, Zsolt Pajor-Gyulai","submitted_at":"2010-09-03T15:30:21Z","abstract_excerpt":"Let $\\{X_n\\}_{n\\in\\mathbb{N}}$ be a sequence of i.i.d. random variables in $\\mathbb{Z}^d$. Let $S_k=X_1+...+X_k$ and $Y_n(t)$ be the continuous process on $[0,1]$ for which $Y_n(k/n)=S_k/\\sqrt{n}$ $k=1,...,n$ and which is linearly interpolated elsewhere. The paper gives a generalization of results of Belkin, \\cite{B72} on the weak limit laws of $Y_n(t)$ conditioned to stay away from some small sets. In particular, it is shown that the diffusive limit of the random walk meander on $\\mathbb Z^d: d\\ge 2$ is the Brownian motion."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.0700","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"}