{"paper":{"title":"Number rigidity in superhomogeneous random point fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Joel Lebowitz, Subhro Ghosh","submitted_at":"2016-01-16T21:55:12Z","abstract_excerpt":"We give sufficient conditions for the number rigidity of a translation invariant or periodic point process on $\\mathbb{R}^d$, where $d=1,2$. That is, the probability distribution of the number of particles in a bounded domain $\\Lambda \\subset \\mathbb{R}^d$, conditional on the configuration on $\\Lambda^\\complement$, is concentrated on a single integer $N_\\Lambda$. These conditions are : (a) the variance of the number of particles in a bounded domain $\\mathcal{O} \\subset \\mathbb{R}^d$ grows slower than the volume of $\\mathcal{O}$ (a.k.a. superhomogeneous point processes), when $\\mathcal{O} \\upar"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.04216","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"}