{"paper":{"title":"Localization-delocalization phenomena for random interfaces","license":"","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Erwin Bolthausen","submitted_at":"2003-04-24T03:00:26Z","abstract_excerpt":"We consider d-dimensional random surface models which for d=1 are the standard (tied-down) random walks (considered as a random ``string''). In higher dimensions, the one-dimensional (discrete) time parameter of the random walk is replaced by the d-dimensional lattice \\Z^d, or a finite subset of it. The random surface is represented by real-valued random variables \\phi_i, where i is in \\Z^d. A class of natural generalizations of the standard random walk are gradient models whose laws are (formally) expressed as\n  P(d\\phi) = 1/Z \\exp[-\\sum_{|i-j|=1}V(\\phi_i-\\phi_j)] \\prod_i d\\phi_i,\n  V:\\R -> R"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0304366","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"}