{"paper":{"title":"Werner's Measure on Self-Avoiding Loops and Welding","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Angel Chavez, Doug Pickrell","submitted_at":"2014-01-12T21:26:30Z","abstract_excerpt":"Werner's conformally invariant family of measures on self-avoiding loops on Riemann surfaces is determined by a single measure $\\mu_0$ on self-avoiding loops in ${\\mathbb C} \\setminus\\{0\\}$ which surround $0$. Our first major objective is to show that the measure $\\mu_0$ is infinitesimally invariant with respect to conformal vector fields (essentially the Virasoro algebra of conformal field theory). This makes essential use of classical variational formulas of Duren and Schiffer, which we recast in representation theoretic terms for efficient computation. We secondly show how these formulas ca"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.2675","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"}