{"paper":{"title":"Dirichlet random walks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Gerard Letac, Mauro Piccioni","submitted_at":"2013-10-23T16:19:11Z","abstract_excerpt":"This article provides tools for the study of the Dirichlet random walk in $\\mathbb{R}^d$. By this we mean the random variable $W=X_1\\Theta_1+\\cdots+X_n\\Theta_n$ where $X=(X_1,\\ldots,X_n) \\sim \\mathcal{D}(q_1,\\ldots,q_n)$ is Dirichlet distributed and where $\\Theta_1,\\ldots \\Theta_n$ are iid, uniformly distributed on the unit sphere of $\\mathbb{R}^d$ and independent of $X.$ In particular we compute explicitely in a number of cases the distribution of $W.$ Some of our results appear already in the literature, in particular in the papers by G\\'erard Le Ca\\\"{e}r (2010, 2011). In these cases, our pr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.6279","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"}