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- W2077854454 abstract "We consider a family of matrix valued orthogonal polynomials obtained by Pacharoni and Tirao in connection with spherical functions for the pair ($mathrm{SU}(N+1)$, $mathrm{U}(N)$); see [I. Pacharoni and J. A. Tirao, Constr. Approx., 25 (2007), pp. 177–192]. After an appropriate conjugation, we obtain a new family of matrix valued orthogonal polynomials where the corresponding block Jacobi matrix is stochastic and has special probabilistic properties. This gives a highly nontrivial example of a nonhomogeneous quasi-birth-and-death process for which we can explicitly compute its “n-step transition probability matrix” and its invariant distribution. The richness of the mathematical structures involved here allows us to give these explicit results for a several parameter family of quasi-birth-and-death processes with an arbitrary (finite) number of phases. Some of these results are plotted to show the effect that choices of the parameter values have on the invariant distribution." @default.
- W2077854454 created "2016-06-24" @default.
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- W2077854454 date "2008-01-01" @default.
- W2077854454 modified "2023-10-01" @default.
- W2077854454 title "Matrix Valued Orthogonal Polynomials Arising from Group Representation Theory and a Family of Quasi-Birth-and-Death Processes" @default.
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- W2077854454 doi "https://doi.org/10.1137/070697604" @default.
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