{"paper":{"title":"Information geometry and asymptotic geodesics on the space of normal distributions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG","math.IT"],"primary_cat":"cs.IT","authors_text":"Raul Quiroga-Barranco, Wolfgang Globke","submitted_at":"2019-04-29T19:34:58Z","abstract_excerpt":"The family $\\mathcal{N}$ of $n$-variate normal distributions is parameterized by the cone of positive definite symmetric $n\\times n$-matrices and the $n$-dimensional real vector space. Equipped with the Fisher information metric, $\\mathcal{N}$ becomes a Riemannian manifold. As such, it is diffeomorphic, but not isometric, to the Riemannian symmetric space $Pos_1(n+1,\\mathbb{R})$ of unimodular positive definite symmetric $(n+1)\\times(n+1)$-matrices. As the computation of distances in the Fisher metric for $n>1$ presents some difficulties, Lovri\\v{c} et al.~(2000) proposed to use the Killing met"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.12921","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"}