{"paper":{"title":"Entropic repulsion in $|\\nabla \\phi|^p$ surfaces: a large deviation bound for all $p\\geq 1$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Fabio Lucio Toninelli (CNRS, Fabio Martinelli (Roma Tre), Lyon 1), Pietro Caputo (Roma Tre)","submitted_at":"2017-01-12T12:52:25Z","abstract_excerpt":"We consider the $(2+1)$-dimensional generalized solid-on-solid (SOS) model, that is the random discrete surface with a gradient potential of the form $|\\nabla\\phi|^{p}$, where $p\\in [1,+\\infty]$. We show that at low temperature, for a square region $\\Lambda$ with side $L$, both under the infinite volume measure and under the measure with zero boundary conditions around $\\Lambda$, the probability that the surface is nonnegative in $\\Lambda$ behaves like $\\exp(-4\\beta\\tau_{p,\\beta} L H_p(L) )$, where $\\beta$ is the inverse temperature, $\\tau_{p,\\beta}$ is the surface tension at zero tilt, or ste"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.03327","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"}