{"paper":{"title":"Hausdorff dimension of affine random covering sets in torus","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.PR","authors_text":"Bing Li, Esa J\\\"arvenp\\\"a\\\"a, Henna Koivusalo, Maarit J\\\"arvenp\\\"a\\\"a, Ville Suomala","submitted_at":"2012-07-16T10:01:25Z","abstract_excerpt":"We calculate the almost sure Hausdorff dimension of the random covering set $\\limsup_{n\\to\\infty}(g_n + \\xi_n)$ in $d$-dimensional torus $\\mathbb T^d$, where the sets $g_n\\subset\\mathbb T^d$ are parallelepipeds, or more generally, linear images of a set with nonempty interior, and $\\xi_n\\in\\mathbb T^d$ are independent and uniformly distributed random points. The dimension formula, derived from the singular values of the linear mappings, holds provided that the sequences of the singular values are decreasing."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.3615","kind":"arxiv","version":2},"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"}