{"paper":{"title":"Spectra of Poisson functionals and applications in continuum percolation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Chinmoy Bhattacharjee, D. Yogeshwaran, Giovanni Peccati","submitted_at":"2024-07-18T13:33:57Z","abstract_excerpt":"Let $\\eta$ be a Poisson random measure (defined on some Polish space), and let $F(\\eta)$ be a square-integrable functional of $\\eta$. In this paper we define and study a new notion of {\\it spectral point process} associated with $F(\\eta)$, and use such an object to study sharp noise instability and sensitivity properties of planar critical continuum percolation models under spatial birth-death (Ornstein-Uhlenbeck) dynamics -- the notion of sharp noise instability being a natural strengthening of the absence of noise stability. The concept of spectral point process is defined by exploiting the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.13502","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2407.13502/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"}