{"paper":{"title":"Packing dimension of images and graphs of Gaussian random fields with drift","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.PR","authors_text":"Rich\\'ard Balka","submitted_at":"2016-10-20T16:04:10Z","abstract_excerpt":"Let $X=\\{(X_1(t),\\dots,X_d(t)): t\\in \\mathbb{R}^n\\}$ be a Gaussian random field in $\\mathbb{R}^d$ such that $X_1,\\dots,X_d$ are independent, centered Gaussian random fields with continuous sample paths. Let $f\\colon \\mathbb{R}^n\\to \\mathbb{R}^d$ be a Borel map and let $A\\subset \\mathbb{R}^n$ be an analytic set. The main goal of the paper is to determine the almost sure value of the packing dimension of the image and graph of $X+f$ restricted to $A$ under a very mild assumption. This generalizes a result of Du, Miao, Wu and Xiao, who calculated the packing dimension of $X(A)$ if $X_1,\\dots,X_d$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.06474","kind":"arxiv","version":3},"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"}