{"paper":{"title":"The Dirichlet curve of a probability in $\\mathbb{R}^d$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Gerard Letac, Mauro Piccioni","submitted_at":"2014-05-19T14:34:34Z","abstract_excerpt":"If $\\alpha$ is a probability on $\\mathbb{R}^d$ and $t>0,$ consider the Dirichlet random probability $P_t\\sim\\mathcal{D}(t\\alpha) ;$ it is such that for any measurable partition $(A_0,\\ldots,A_k)$ of $\\mathbb{R}^d$ then $(P_t(A_0),\\ldots,P_t(A_k))$ is Dirichlet distributed with parameters $(t\\alpha(A_0)\\ldots,t\\alpha(A_k)).$ If $\\int_{\\mathbb{R}^d}\\log(1+\\|x\\|)\\alpha(dx)<\\infty$ the random variable $\\int_{\\mathbb{R}^d}xP_t(dx)$ of $\\mathbb{R}^d$ does exist and we denote by $\\mu(t\\alpha)$ its distribution. The Dirichlet curve associated to the probability $\\alpha$ is the map $t\\mapsto \\mu(t\\alph"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.4744","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"}