{"paper":{"title":"Processes of rth Largest","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Boris Buchmann, Ross Maller, Sidney Resnick","submitted_at":"2016-07-29T01:29:18Z","abstract_excerpt":"For integers $n\\geq r$, we treat the $r$th largest of a sample of size $n$ as an $\\mathbb{R}^\\infty$-valued stochastic process in $r$ which we denote $\\mathbf{M}^{(r)}$. We show that the sequence regarded in this way satisfies the Markov property. We go on to study the asymptotic behaviour of $\\mathbf{M}^{(r)}$ as $r\\to\\infty$, and, borrowing from classical extreme value theory, show that left-tail domain of attraction conditions on the underlying distribution of the sample guarantee weak limits for both the range of $\\mathbf{M}^{(r)}$ and $\\mathbf{M}^{(r)}$ itself, after norming and centering"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.08674","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"}