{"paper":{"title":"Nesting of double-dimer loops: local fluctuations and convergence to the nesting field of CLE(4)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","math.PR"],"primary_cat":"math-ph","authors_text":"Konstantin Izyurov, Mikhail Basok","submitted_at":"2025-01-02T23:40:50Z","abstract_excerpt":"We consider the double-dimer model in the upper-half plane discretized by the square lattice with mesh size $\\delta$. For each point $x$ in the upper half-plane, we consider the random variable $N_\\delta(x)$ given by the number of the double-dimer loops surrounding this point. We prove that the normalized fluctuations of $N_\\delta(x)$ for a fixed $x$ are asymptotically Gaussian as $\\delta\\to 0+$. Further, we prove that the double-dimer nesting field $N_\\delta(\\cdot) - \\mathbb{E}\\, N_\\delta(\\cdot)$, viewed as a random distribution in the upper half-plane, converges as $\\delta\\to 0+$ to the nest"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.01574","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/2501.01574/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"}