{"paper":{"title":"SLE$_{\\kappa}(\\rho)$ processes in the light cone regime on Liouville quantum gravity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Jason Miller, Konstantinos Kavvadias","submitted_at":"2024-12-05T09:29:56Z","abstract_excerpt":"We study the relationship between certain SLE$_\\kappa(\\rho)$ processes, which are variants of the Schramm-Loewner evolution with parameter $\\kappa$ in which one keeps track of an extra marked point, and Liouville quantum gravity (LQG). These processes are defined whenever $\\rho > -2-\\kappa/2$ and in this work we will focus on the light cone regime, meaning that $\\kappa \\in (0,4)$ and $\\max(\\kappa/2-4,-2-\\kappa/2) < \\rho < -2$. Such processes are self-intersecting even though ordinary SLE$_\\kappa$ curves are simple for $\\kappa \\in (0,4)$. We show that such a process drawn on top of an independe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.04005","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/2412.04005/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"}