{"paper":{"title":"Flying randomly in $\\mathbb{R}^d$ with Dirichlet displacements","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Alessandro De Gregorio, Enzo Orsingher","submitted_at":"2011-07-29T09:52:41Z","abstract_excerpt":"Random flights in $\\mathbb{R}^d,d\\geq 2,$ with Dirichlet-distributed displacements and uniformly distributed orientation are analyzed. The explicit characteristic functions of the position $\\underline{\\bf X}_d(t),\\,t>0,$ when the number of changes of direction is fixed are obtained. The probability distributions are derived by inverting the characteristic functions for all dimensions $d$ of $\\mathbb{R}^d$ and many properties of the probabilistic structure of $\\underline{\\bf X}_d(t),t>0,$ are examined.\n  If the number of changes of direction is randomized by means of a fractional Poisson proces"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.5913","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"}