Autor(en): | Rösler, Margit Voit, Michael |
Titel: | A central limit theorem for random walks on the dual of a compact Grassmannian |
Sprache (ISO): | en |
Zusammenfassung: | 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. |
Schlagwörter: | Mehler-Heine formula Heckman-Opdam polynomials Grassmann manifolds spherical functions central limit theorem asymptotic representation theory |
URI: | http://hdl.handle.net/2003/33759 http://dx.doi.org/10.17877/DE290R-6708 |
Erscheinungsdatum: | 2014-12 |
Enthalten in den Sammlungen: | Preprints der Fakultät für Mathematik |
Dateien zu dieser Ressource:
Datei | Beschreibung | Größe | Format | |
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Preprint 2014-07.pdf | 331.14 kB | Adobe PDF | Öffnen/Anzeigen |
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