{"paper":{"title":"A continuous proof of the existence of the SLE$_8$ curve","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.CV","math.MP"],"primary_cat":"math.PR","authors_text":"Jason Miller, Valeria Ambrosio","submitted_at":"2022-03-25T17:51:32Z","abstract_excerpt":"Suppose that $\\eta$ is a whole-plane space-filling SLE$_\\kappa$ for $\\kappa \\in (4,8)$ from $\\infty$ to $\\infty$ parameterized by Lebesgue measure and normalized so that $\\eta(0) = 0$. For each $T > 0$ and $\\kappa \\in (4,8)$ we let $\\mu_{\\kappa,T}$ denote the law of $\\eta|_{[0,T]}$. We show for each $\\nu, T > 0$ that the family of laws $\\mu_{\\kappa,T}$ for $\\kappa \\in [4+\\nu,8)$ is compact in the weak topology associated with the space of probability measures on continuous curves $[0,T] \\to {\\mathbf C}$ equipped with the uniform distance. As a direct byproduct of this tightness result (taking "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2203.13805","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2203.13805/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}