{"paper":{"title":"Asymptotic Analysis of the Ginzburg-Landau Functional on Point Clouds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Florian Theil, Matthew Thorpe","submitted_at":"2016-04-17T21:15:56Z","abstract_excerpt":"The Ginzburg-Landau functional is a phase transition model which is suitable for clustering or classification type problems. We study the asymptotics of a sequence of Ginzburg-Landau functionals with anisotropic interaction potentials on point clouds $\\Psi_n$ where $n$ denotes the number data points. In particular we show the limiting problem, in the sense of $\\Gamma$-convergence, is related to the total variation norm restricted to functions taking binary values; which can be understood as a surface energy. We generalize the result known for isotropic interaction potentials to the anisotropic"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.04930","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"}