{"paper":{"title":"Invariance principle for non-homogeneous random walks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Aleksandar Mijatovi\\'c, Andrew R. Wade, Nicholas Georgiou","submitted_at":"2018-01-24T07:22:17Z","abstract_excerpt":"We prove an invariance principle for a class of zero-drift spatially non-homogeneous random walks in $\\mathbb{R}^d$, which may be recurrent in any dimension. The limit $\\mathcal{X}$ is an elliptic martingale diffusion, which may be point-recurrent at the origin for any $d\\geq2$. To characterise $\\mathcal{X}$, we introduce a (non-Euclidean) Riemannian metric on the unit sphere in $\\mathbb{R}^d$ and use it to express a related spherical diffusion as a Brownian motion with drift. This representation allows us to establish the skew-product decomposition of the excursions of $\\mathcal{X}$ and thus "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.07882","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"}