{"paper":{"title":"Normal approximation for the net flux through a random conductor","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.PR","authors_text":"James Nolen","submitted_at":"2014-06-09T14:16:04Z","abstract_excerpt":"We consider solutions to an elliptic partial differential equation in $\\mathbb{R}^d$ with a stationary, random conductivity coefficient. The boundary condition on a square domain of width $L$ is chosen so that the solution has a macroscopic unit gradient. We then consider the average flux through the domain. It is known that in the limit $L \\to \\infty$, this quantity converges to a deterministic constant, almost surely. Our main result is about normal approximation for this flux when $L$ is large: we give an estimate of the Kantorovich-Wasserstein distance between the law of this random variab"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.2186","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":""},"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"}