Authors: Artykov, MerdanVoit, Michael Title: Some central limit theorems for random walks associated with hypergeometric functions of type BC Language (ISO): en Abstract: The spherical functions of the noncompact Grassmann manifolds $G_{p,q}(\mathbb F)=G/K$ over $\mathbb F=\mathbb R, \mathbb C, \mathbb H$ with rank $q\ge1$ and dimension parameter $p>q$ are Heckman-Opdam hypergeometric functions of type BC, when the double coset spaces $G//K$ are identified with the Weyl chamber $C_q^B\subset \mathbb R^q$ of type B. The associated double coset hypergroups on $C_q^B$ can be embedded into a continuous family of commutative hypergroups $(C_q^B,*_p)$ with $p\in[2q-1,\infty[$ associated with these hypergeometric functions by Rösler. Several limit theorems for random walks on these hypergroups were recently derived by Voit (2017). We here present further limit theorems when the time as well as $p$ tend to $\infty$. For integers $p$, this admits interpretations for group-invariant random walks on the Grassmannians $G/K$. Subject Headings: hypergeometric functions associated with root systemsHeckman-Opdam theorynoncompact Grassmann manifoldsspherical functionsrandom walks on symmetric spacesrandom walks on hypergroupsmoment functionscentral limit theoremsdimension to infinity URI: http://hdl.handle.net/2003/38163http://dx.doi.org/10.17877/DE290R-20142 Issue Date: 2018-02 Appears in Collections: Preprints der Fakultät für Mathematik

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