{"paper":{"title":"Remarks on the intersection of SLE$_{\\kappa}(\\rho)$ curve with the real line","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Hao Wu, Menglu Wang","submitted_at":"2015-07-01T13:11:08Z","abstract_excerpt":"SLE$_{\\kappa}(\\rho)$ is a variant of SLE$_{\\kappa}$ where $\\rho$ characterizes the repulsion (if $\\rho>0$) or attraction $(\\rho<0)$ from the boundary. This paper examines the probabilities of SLE$_{\\kappa}(\\rho)$ to get close to the boundary. We show how close the chordal SLE$_{\\kappa}(\\rho)$ curves get to the boundary asymptotically, and provide an estimate for the probability that the SLE$_{\\kappa}(\\rho)$ curve hits graph of functions. These generalize the similar result derived by Schramm and Zhou for standard SLE$_{\\kappa}$ curves."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.00218","kind":"arxiv","version":3},"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"}