{"paper":{"title":"Moments of quantum L\\'evy areas using sticky shuffle Hopf algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Robin Hudson, Uwe Schauz, Yue Wu","submitted_at":"2016-05-03T02:07:35Z","abstract_excerpt":"We study a family of quantum analogs of L\\'evy's stochastic area for planar Brownian motion depending on a variance parameter $\\sigma \\geq 1$ which deform to the classical L\\'evy area as $\\sigma\\rightarrow\\infty$. They are defined as second rank iterated stochastic integrals against the components of planar Brownian motion, which are one-dimensional Brownian motions satisfying Heisnberg-type commutation relations. Such iterated integrals can be multiplied using the sticky shuffle product determined by the underlying It\\^o algebra of stochastic differentials. We use the corresponding Hopf algeb"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.00730","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"}