{"paper":{"title":"A strong central limit theorem for a class of random surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Joseph G. Conlon, Thomas Spencer","submitted_at":"2011-05-13T19:43:34Z","abstract_excerpt":"This paper is concerned with $d=2$ dimensional lattice field models with action $V(\\na\\phi(\\cdot))$, where $V:\\R^d\\ra \\R$ is a uniformly convex function. The fluctuations of the variable $\\phi(0)-\\phi(x)$ are studied for large $|x|$ via the generating function given by $g(x,\\mu) = \\ln <e^{\\mu(\\phi(0) - \\phi(x))}>_{A}$. In two dimensions $g\"(x,\\mu)=\\pa^2g(x,\\mu)/\\pa\\mu^2$ is proportional to $\\ln|x|$. The main result of this paper is a bound on $g\"'(x,\\mu)=\\pa^3 g(x,\\mu)/\\pa \\mu^3$ which is uniform in $|x|$ for a class of convex $V$.\n  The proof uses integration by parts following Helffer-Sj\\\"{o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.2814","kind":"arxiv","version":3},"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"}