{"paper":{"title":"Higher Conformal Multifractality","license":"","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"Bertrand Duplantier","submitted_at":"2002-07-31T17:52:28Z","abstract_excerpt":"We derive, from conformal invariance and quantum gravity, the multifractal spectrum f(alpha,c) of the harmonic measure (or electrostatic potential, or diffusion field) near any conformally invariant fractal in two dimensions, corresponding to a conformal field theory of central charge c. It gives the Hausdorff dimension of the set of boundary points where the potential varies with distance r to the fractal frontier as r^{alpha}. First examples are a Brownian frontier, a self-avoiding walk, or a percolation cluster. Potts, O(N) models, and the so-called SLE process are also considered. Higher m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/0207743","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"}