Authors: Rösler, Margit
Voit, Michael
Title: A central limit theorem for random walks on the dual of a compact Grassmannian
Language (ISO): en
Abstract: We consider compact Grassmann manifolds G/K over the real, complex or quaternionic numbers whose spherical functions are Heckman-Opdam polynomials of type BC. From an explicit integral representation of these polynomials we deduce a sharp Mehler-Heine formula, that is an approximation of the Heckman-Opdam polynomials in terms of Bessel functions, with a precise estimate on the error term. This result is used to derive a central limit theorem for random walks on the semi-lattice parametrizing the dual of G/K, which are constructed by successive decompositions of tensor powers of spherical representations of G. The limit is the distribution of a Laguerre ensemble in random matrix theory. Most results of this paper are established for a larger continuous set of multiplicity parameters beyond the group cases.
Subject Headings: Mehler-Heine formula
Heckman-Opdam polynomials
Grassmann manifolds
spherical functions
central limit theorem
asymptotic representation theory
Issue Date: 2014-12
Appears in Collections:Preprints der Fakultät für Mathematik

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