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This article is cited in 2 scientific papers (total in 2 papers)
A Central Limit Theorem for Random Walks on the Dual of a Compact Grassmannian
Margit Röslera, Michael Voitb a Institut für Mathematik, Universität Paderborn, Warburger Str. 100, D-33098 Paderborn, Germany
b Fakultät für Mathematik, Technische Universität Dortmund, Vogelpothsweg 87, D-44221 Dortmund, Germany
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.
Keywords:
Mehler–Heine formula; Heckman–Opdam polynomials; Grassmann manifolds; spherical functions; central limit
theorem; asymptotic representation theory.
Received: October 14, 2014; in final form February 3, 2015; Published online February 10, 2015
Citation:
Margit Rösler, Michael Voit, “A Central Limit Theorem for Random Walks on the Dual of a Compact Grassmannian”, SIGMA, 11 (2015), 013, 18 pp.
Linking options:
https://www.mathnet.ru/eng/sigma994 https://www.mathnet.ru/eng/sigma/v11/p13
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