Authors: Artykov, Merdan
Voit, 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 systems
Heckman-Opdam theory
noncompact Grassmann manifolds
spherical functions
random walks on symmetric spaces
random walks on hypergroups
moment functions
central limit theorems
dimension to infinity
Issue Date: 2018-02
Appears in Collections:Preprints der Fakultät für Mathematik

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