{"paper":{"title":"Absolute continuity and singularity of Palm measures of the Ginibre point process","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Hirofumi Osada, Tomoyuki Shirai","submitted_at":"2014-06-16T06:09:53Z","abstract_excerpt":"We prove a dichotomy between absolute continuity and singularity of the Ginibre point process $\\mathsf{G}$ and its reduced Palm measures $\\{\\mathsf{G}_{\\mathbf{x}}, \\mathbf{x} \\in \\mathbb{C}^{\\ell}, \\ell = 0,1,2\\dots\\}$, namely, reduced Palm measures $\\G_{\\mathbf{x}}$ and $\\G_{\\mathbf{y}}$ for $\\mathbf{x} \\in \\mathbb{C}^{\\ell}$ and $\\mathbf{y} \\in \\mathbb{C}^{n}$ are mutually absolutely continuous if and only if $\\ell = n$; they are singular each other if and only if $\\ell \\not= n$. Furthermore, we give an explicit expression of the Radon-Nikodym density\n  $d\\G_{\\mathbf{x}}/d \\G_{\\mathbf{y}}$ "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.3913","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"}