{"paper":{"title":"On Multivariate Records from Random Vectors with Independent Components","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"A. Khorrami, M. Falk, S. A. Padoan","submitted_at":"2017-07-25T16:13:24Z","abstract_excerpt":"Let $\\boldsymbol{X}_1,\\boldsymbol{X}_2,\\dots$ be independent copies of a random vector $\\boldsymbol{X}$ with values in $\\mathbb{R}^d$ and with a continuous distribution function. The random vector $\\boldsymbol{X}_n$ is a complete record, if each of its components is a record. As we require $\\boldsymbol{X}$ to have independent components, crucial results for univariate records clearly carry over. But there are substantial differences as well: While there are infinitely many records in case $d=1$, there occur only finitely many in the series if $d\\geq 2$. Consequently, there is a terminal comple"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.08065","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"}