{"paper":{"title":"A Liouville principle for the random conductance model under degenerate conditions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.NA","math.PR"],"primary_cat":"math.AP","authors_text":"Tuan Anh Nguyen","submitted_at":"2019-08-28T12:44:29Z","abstract_excerpt":"We consider a random conductance model on the $d$-dimensional lattice, $d\\in[2,\\infty)\\cap\\mathbb{N}$, where the conductances take values in $(0,\\infty)$ and are however not assumed to be bounded from above and below. We assume that the law of the random conductances is stationary and ergodic with respect to translations on $\\mathbb{Z}^d$ and invariant with respect to reflections on $\\mathbb{Z}^d$ and satisfies a similar moment bound as that by Andres, Deuschel, and Slowik (2015), under which a quenched FCLT holds. We prove a first-order Liouville theorem. In the proof we construct the subline"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.10691","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/1908.10691/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"}