{"paper":{"title":"Dimensions of random covering sets in Riemann manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.PR"],"primary_cat":"math.CA","authors_text":"De-Jun Feng, Esa J\\\"arvenp\\\"a\\\"a, Maarit J\\\"arvenp\\\"a\\\"a, Ville Suomala","submitted_at":"2015-08-31T15:55:24Z","abstract_excerpt":"Let ${\\pmb M}$, ${\\pmb N}$ and ${\\pmb K}$ be $d$-dimensional Riemann manifolds. Assume that ${\\bf A}:=(A_n)_{n\\in{\\Bbb N}}$ is a sequence of Lebesgue measurable subsets of ${\\pmb M}$ satisfying a necessary density condition and ${\\bf x}:=(x_n)_{n\\in {\\Bbb N}}$ is a sequence of independent random variables which are distributed on ${\\pmb K}$ according to a measure which is not purely singular with respect to the Riemann volume. We give a formula for the almost sure value of the Hausdorff dimension of random covering sets ${\\bf E}({\\bf x},{\\bf A}):=\\limsup_{n\\to\\infty}A_n(x_n)\\subset {\\pmb N}$. "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.07881","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"}