{"paper":{"title":"A contour line of the continuum Gaussian free field","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Oded Schramm, Scott Sheffield","submitted_at":"2010-08-14T13:54:21Z","abstract_excerpt":"Consider an instance $h$ of the Gaussian free field on a simply connected planar domain with boundary conditions $-\\lambda$ on one boundary arc and $\\lambda$ on the complementary arc, where $\\lambda$ is the special constant $\\sqrt{\\pi/8}$. We argue that even though $h$ is defined only as a random distribution, and not as a function, it has a well-defined zero contour line connecting the endpoints of these arcs, whose law is SLE(4). We construct this contour line in two ways: as the limit of the chordal zero contour lines of the projections of $h$ onto certain spaces of piecewise linear functio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.2447","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"}