{"paper":{"title":"Critical Ising model, Multiple SLE$_\\kappa\\left(\\frac{\\kappa-6}{2},\\frac{\\kappa-6}{2}\\right)$ and $\\beta$-Jacobi Ensemble","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Mingchang Liu","submitted_at":"2025-04-20T12:51:59Z","abstract_excerpt":"Fix $N\\ge 1$ and suppose that $(\\Omega;x_1,\\ldots, x_{N}; x_{N+1}, x_{N+2})$ is a polygon, i.e. $\\Omega$ is a simply connected domain with locally connected boundary and $x_1,\\ldots,x_{N+2}$ are $N+2$ different points located counterclockwisely on $\\partial\\Omega$. Fix $\\kappa\\in (0,4)$. In this paper, we will give two different constructions of multiple $N$-SLE$_\\kappa\\left(\\frac{\\kappa-6}{2},\\frac{\\kappa-6}{2}\\right)$ on $(\\Omega;x_1,\\ldots,x_{N}; x_{N+1},x_{N+2})$ and prove that they give the same law on random curves. Then, by establishing the uniqueness of multiple $N$-SLE$_\\kappa\\left(\\f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.14595","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/2504.14595/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"}