Rösler, MargitVoit, Michael2014-12-022014-12-022014-12http://hdl.handle.net/2003/3375910.17877/DE290R-6708We 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.enPreprint; 2014-07Mehler-Heine formulaHeckman-Opdam polynomialsGrassmann manifoldsspherical functionscentral limit theoremasymptotic representation theory610preprint