{"paper":{"title":"Multivariate normal approximation in geometric probability","license":"","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Andrew R. Wade, Mathew D. Penrose","submitted_at":"2007-07-26T11:10:48Z","abstract_excerpt":"Consider a measure $\\mu_\\lambda = \\sum_x \\xi_x \\delta_x$ where the sum is over points $x$ of a Poisson point process of intensity $\\lambda$ on a bounded region in $d$-space, and $\\xi_x$ is a functional determined by the Poisson points near to $x$, i.e. satisfying an exponential stabilization condition, along with a moments condition (examples include statistics for proximity graphs, germ-grain models and random sequential deposition models). A known general result says the $\\mu_\\lambda$-measures (suitably scaled and centred) of disjoint sets in $R^d$ are asymptotically independent normals as $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0707.3898","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"}