{"paper":{"title":"Necessary and sufficient conditions for realizability of point processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Eugene R. Speer, Joel L. Lebowitz, Tobias Kuna","submitted_at":"2009-10-09T11:09:52Z","abstract_excerpt":"We give necessary and sufficient conditions for a pair of (generalized) functions $\\rho_1(\\mathbf{r}_1)$ and $\\rho_2(\\mathbf{r}_1,\\mathbf{r}_2)$, $\\mathbf{r}_i\\in X$, to be the density and pair correlations of some point process in a topological space $X$, for example, $\\mathbb {R}^d$, $\\mathbb {Z}^d$ or a subset of these. This is an infinite-dimensional version of the classical \"truncated moment\" problem. Standard techniques apply in the case in which there can be only a bounded number of points in any compact subset of $X$. Without this restriction we obtain, for compact $X$, strengthened co"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0910.1710","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"}