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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."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1009.0700","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-09-03T15:30:21Z","cross_cats_sorted":[],"title_canon_sha256":"c78418fc8bb7270420ab80a80dcd49284a39a4f7b8a77f1b7b89f8ccc033ed49","abstract_canon_sha256":"64f6dcc1217df1a712a0553fa1c03eb2a4f2741a7684f7e95dfa3df3812476f8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:41:25.606452Z","signature_b64":"qESWTbYEGA9tdzMpJitLoXI8xNlewwssCtUuGe/SRAArJIGSLKFgI6UUXPvtVRqlBHgFrAWxqlOCaCOf/LjIAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"51f8e3ae6163fb0d176f3639128a991ddfa0700b12b7593a5b738dcade8adffe","last_reissued_at":"2026-05-18T04:41:25.605801Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:41:25.605801Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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 $\\mathbb{Z}^d$. 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