{"paper":{"title":"Cluster point processes on manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.FA","authors_text":"Alexei Daletskii, Leonid Bogachev","submitted_at":"2011-09-28T18:16:13Z","abstract_excerpt":"The probability distribution $\\mu_{cl}$ of a general cluster point process in a Riemannian manifold $X$ (with independent random clusters attached to points of a configuration with distribution $\\mu$) is studied via the projection of an auxiliary measure $\\hat{\\mu}$ in the space of configurations $\\hat{\\gamma}=\\{(x,\\bar{y})\\}\\subset X\\times\\mathfrak{X}$, where $x\\in X$ indicates a cluster \"centre\" and $\\bar{y}\\in\\mathfrak{X}:=\\bigsqcup_{n} X^n$ represents a corresponding cluster relative to $x$. We show that the measure $\\mu_{cl}$ is quasi-invariant with respect to the group $Diff_{0}(X)$ of c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.6283","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"}