{"paper":{"title":"Non-commutative L\\'evy processes for generalized (particularly anyon) statistics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Eugene Lytvynov, Janusz Wysoczanski, Marek Bozejko","submitted_at":"2011-06-15T10:53:54Z","abstract_excerpt":"Let $T=\\mathbb R^d$. Let a function $Q:T^2\\to\\mathbb C$ satisfy $Q(s,t)=\\bar{Q(t,s)}$ and $|Q(s,t)|=1$. A generalized statistics is described by creation operators $\\partial_t^\\dag$ and annihilation operators $\\partial_t$, $t\\in T$, which satisfy the $Q$-commutation relations. From the point of view of physics, the most important case of a generalized statistics is the anyon statistics, for which $Q(s,t)$ is equal to $q$ if $s<t$, and to $\\bar q$ if $s>t$. Here $q\\in\\mathbb C$, $|q|=1$. We start the paper with a detailed discussion of a $Q$-Fock space and operators $(\\partial_t^\\dag,\\partial_t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.2933","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"}