{"paper":{"title":"Hyperuniform random measures, transport and rigidity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"MATHNET), Rapha\\\"el Lachi\\`eze-Rey (MAP5 - UMR 8145","submitted_at":"2025-10-21T08:13:03Z","abstract_excerpt":"This survey explores the foundational theory and recent developments in the study of hyperuniformity. We present a comprehensive mathematical framework in the context of weakly stationary random measures, emphasizing spectral characterizations and second order asymptotics. Classical examples - including determinantal point processes, Gibbs measures, and zero sets of Gaussian analytic functions - are presented in depth to illustrate core principles. We also highlight recent progress connecting hyperuniformity with optimal transport and rigidity phenomena, pointing to emerging directions in the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2510.18392","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2510.18392/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}