{"paper":{"title":"Wetting transitions for a random line in long-range potential","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"F. Dunlop, P. Collet, T. Huillet","submitted_at":"2014-11-19T07:30:07Z","abstract_excerpt":"We consider a restricted Solid-on-Solid interface in $\\Bbb{Z}_{+}$, subject to a potential $V\\left( n\\right) $ behaving at infinity like $-\\mathrm{w}/n^{2}$. Whenever there is a wetting transition as $b_{0}\\equiv \\exp V\\left( 0\\right) $ is varied, we prove the following results for the density of returns $m\\left( b_{0}\\right) $ to the origin: if $\\mathrm{w}<-3/8$, then $m\\left( b_{0}\\right) $ has a jump at $b_{0}^{c}$; if $-3/8<\\mathrm{w}<1/8$, then $m\\left( b_{0}\\right) \\sim \\left( b_{0}^{c}-b_{0}\\right) ^{\\theta /\\left( 1-\\theta \\right) }$ where $\\theta =1-\\frac{\\sqrt{1-8\\mathrm{w}}}{2}$; if"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.5130","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":""},"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"}