{"paper":{"title":"Markov semi-groups associated with the complex unimodular group $Sl(2,\\mathbb{C})$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.PR","authors_text":"Nizar Demni","submitted_at":"2018-07-24T17:20:09Z","abstract_excerpt":"In this paper, we derive the explicit expressions of two Markov semi-groups constructed by P. Biane in \\cite{Bia1} from the restriction of a particular positive definite function on the complex unimodular group $Sl(2,\\mathbb{C})$ to two commutative subalgebras of its universal $C^{\\star}$-algebra. Our computations use Euclidean Fourier analysis together with the generating function of Laguerre polynomials with index $-1$, and yield absolutely-convergent double series representations of the semi-group densities. In the last part of the paper, we discuss the coincidence, noticed by Biane as well"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.09238","kind":"arxiv","version":3},"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"}