{"paper":{"title":"Stochastic Komatu-Loewner evolutions and SLEs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Hiroyuki Suzuki, Masatoshi Fukushima, Zhen-Qing Chen","submitted_at":"2016-04-28T00:50:37Z","abstract_excerpt":"Let $D={\\mathbb H}\\setminus \\bigcup_{j=1}^N C_j$ be a standard slit domain, where ${\\mathbb H}$ is the upper half plane and $C_j,1\\le j\\le N,$ are mutually disjoint horizontal line segments in ${\\mathbb H}$. A stochastic Komatu-Loewner evolution denoted by ${\\rm SKLE}_{\\alpha,b}$ has been introduced in \\cite{CF} as a family $\\{F_t\\}$ of random growing hulls with $F_t\\subset D$ driven by a diffusion process $\\xi(t)$ on $\\partial {\\mathbb H}$ that is determined by certain continuous homogeneous functions $\\alpha$ and $b$ defined on the space ${\\cal S}$ of all labelled standard slit domains. We a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.08276","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"}