{"paper":{"title":"Reach of Repulsion for Determinantal Point Processes in High Dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Eliza O'Reilly, Fran\\c{c}ois Baccelli","submitted_at":"2017-05-09T20:00:10Z","abstract_excerpt":"Goldman [7] proved that the distribution of a stationary determinantal point process (DPP) $\\Phi$ can be coupled with its reduced Palm version $\\Phi^{0,!}$ such that there exists a point process $\\eta$ where $\\Phi = \\Phi^{0,!} \\cup \\eta$ in distribution and $\\Phi^{0,!} \\cap \\eta = \\emptyset$. The points of $\\eta$ characterize the repulsive nature of a typical point of $\\Phi$. In this paper, the first moment measure of $\\eta$ is used to study the repulsive behavior of DPPs in high dimensions. It is shown that many families of DPPs have the property that the total number of points in $\\eta$ conv"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.03515","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"}