{"paper":{"title":"The Multifractal Spectra of V-Statistics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Ai-Hua Fan (LAMFA), Joerg Schmeling, Meng Wu (LAMFA)","submitted_at":"2012-06-14T19:01:47Z","abstract_excerpt":"Let $(X, T)$ be a topological dynamical system and let $\\Phi: X^r \\to \\mathbb{R}$ be a continuous function on the product space $X^r= X\\times ... \\times X$ ($r\\ge 1$). We are interested in the limit of V-statistics taking $\\Phi$ as kernel: [\\lim_{n\\to \\infty} n^{-r}\\sum_{1\\le i_1, ..., i_r\\le n} \\Phi(T^{i_1}x, ..., T^{i_r} x).] The multifractal spectrum of topological entropy of the above limit is expressed by a variational principle when the system satisfies the specification property. Unlike the classical case ($r=1$) where the spectrum is an analytic function when $\\Phi$ is H\\\"{o}lder conti"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.3214","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"}