A central limit theorem for random walks on the dual of a compact Grassmannian
| dc.contributor.author | Rösler, Margit | |
| dc.contributor.author | Voit, Michael | |
| dc.date.accessioned | 2014-12-02T15:52:14Z | |
| dc.date.available | 2014-12-02T15:52:14Z | |
| dc.date.issued | 2014-12 | |
| dc.description.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. | en |
| dc.identifier.uri | http://hdl.handle.net/2003/33759 | |
| dc.identifier.uri | http://dx.doi.org/10.17877/DE290R-6708 | |
| dc.language.iso | en | |
| dc.relation.ispartofseries | Preprint; 2014-07 | en |
| dc.subject | Mehler-Heine formula | en |
| dc.subject | Heckman-Opdam polynomials | en |
| dc.subject | Grassmann manifolds | en |
| dc.subject | spherical functions | en |
| dc.subject | central limit theorem | en |
| dc.subject | asymptotic representation theory | en |
| dc.subject.ddc | 610 | |
| dc.title | A central limit theorem for random walks on the dual of a compact Grassmannian | en |
| dc.type | Text | de |
| dc.type.publicationtype | preprint | en |
| dcterms.accessRights | open access |