{"paper":{"title":"Logarithmic Coefficients and Generalized Multifractality of Whole-Plane SLE","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","math.CV","math.MP","math.PR"],"primary_cat":"math-ph","authors_text":"Bertrand Duplantier, Michel Zinsmeister, Thanh Binh Le, Xuan Hieu Ho","submitted_at":"2015-04-21T19:55:19Z","abstract_excerpt":"We consider the whole-plane SLE conformal map f from the unit disk to the slit plane, and show that its mixed moments, involving a power p of the derivative modulus |f'| and a power q of the map |f| itself, have closed forms along some integrability curves in the (p,q) moment plane, which depend continuously on the SLE parameter kappa. The generalization of this integrability property to the m-fold transform of f is also given. We define a generalized integral means spectrum corresponding to the singular behavior of the mixed moments above. By inversion, it allows for a unified description of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.05570","kind":"arxiv","version":2},"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"}