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Annali di Matematica Pura ed Applicata

, Volume 192, Issue 3, pp 447–473 | Cite as

Two stochastic models of a random walk in the U(n)-spherical duals of U(n + 1)

  • F. A. Grünbaum
  • I. Pacharoni
  • J. Tirao
Article

Abstract

The random walk to be considered takes place in the δ-spherical dual of the group U(n + 1), for a fixed finite dimensional irreducible representation δ of U(n). The transition matrix comes from the three-term recursion relation satisfied by a sequence of matrix valued orthogonal polynomials built up from the irreducible spherical functions of type δ of SU(n + 1). One of the stochastic models is an urn model and the other is a Young diagram model.

Keywords

Matrix valued spherical functions Matrix orthogonal polynomials Random walks Urn model Young diagram model 

Mathematics Subject Classification (2000)

22E45 33C45 60G99 60J35 

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Copyright information

© Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag 2011

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of CaliforniaBerkeleyUSA
  2. 2.CIEM-FaMAF, Universidad Nacional de CórdobaCórdobaArgentina

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