{"paper":{"title":"Invisibility of the integers for the discrete Gaussian chain via a Caffarelli-Silvestre extension of the discrete fractional Laplacian","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Christophe Garban","submitted_at":"2023-12-07T18:55:12Z","abstract_excerpt":"The Discrete Gaussian Chain is a model of interfaces $\\Psi : \\mathbf{Z} \\to \\mathbf{Z}$ governed by the Hamiltonian $$ H(\\Psi)= \\sum_{i\\neq j} J_\\alpha(|i-j|) |\\Psi_i -\\Psi_j|^2 $$ with long-range coupling constants $J_\\alpha(k)\\asymp k^{-\\alpha}$. For any $\\alpha\\in [2,3)$ and at high enough temperature, we prove an invariance principle for such an $\\alpha$-Discrete Gaussian Chain towards a $H(\\alpha)$-fractional Gaussian process where the Hurst index $H$ satisfies $H=H(\\alpha)=\\frac {\\alpha-2} 2$. This result goes beyond a conjecture by Fr\\\"ohlich and Zegarlinski [FZ91] which conjectured flu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2312.04536","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/2312.04536/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"}