{"paper":{"title":"Non-intersecting Brownian motions leaving from and going to several points","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Didier Vanderstichelen, Mark Adler, Pierre van Moerbeke","submitted_at":"2010-05-07T22:25:42Z","abstract_excerpt":"Consider n non-intersecting Brownian motions on $\\mathbb{R}$, depending on time $t \\in [0,1]$, with $m_i$ particles forced to leave from $a_i$ at time $t=0$, $1\\leq i\\leq q$, and $n_j$ particles forced to end up at $b_j$ at time $t=1$, $1\\leq j\\leq p$. For arbitrary $p$ and $q$, it is not known if the distribution of the positions of the non-intersecting Brownian particles at a given time $0<t<1$, is the same as the joint distribution of the eigenvalues of a matrix ensemble. This paper proves the existence, for general $p$ and $q$, of a partial differential equation (PDE) satisfied by the log "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1005.1303","kind":"arxiv","version":2},"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"}