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Doubly periodic lozenge tilings of a hexagon and matrix valued orthogonal polynomials. [PDF]
Stud Appl Math, 2021 AbstractWe analyze a random lozenge tiling model of a large regular hexagon, whose underlying weight structure is periodic of period 2 in both the horizontal and vertical directions. This is a determinantal point process whose correlation kernel is expressed in terms of non‐Hermitian matrix valued orthogonal polynomials (OPs).
Charlier C.
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Matrix-valued orthogonal polynomials related to hexagon tilings [PDF]
Journal of Approximation Theory, 2021 In this paper, we study a class of matrix-valued orthogonal polynomials (MVOPs) that are related to 2-periodic lozenge tilings of a hexagon. The general model depends on many parameters. In the cases of constant and $2$-periodic parameter values we show that the MVOP can be expressed in terms of scalar polynomials with non-Hermitian orthogonality on a ...
Groot, Alan, Kuijlaars, Arno B.J.
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Spectral decomposition and matrix-valued orthogonal polynomials [PDF]
Advances in Mathematics, 2013 15 ...
Technische Universiteit Delft, DIAM, EWI, Postbus 5031 GA Delft, The Netherlands ( host institution ) +3 more
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The two periodic Aztec diamond and matrix valued orthogonal polynomials [PDF]
Journal of the European Mathematical Society, 2019 We analyze domino tilings of the two-periodic Aztec diamond by means of matrix valued orthogonal polynomials that we obtain from a reformulation of the Aztec diamond as a non-intersecting path model with periodic transition matrices.
Duits, Maurice, Kuijlaars, Arno B. J.
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A Hypergeometric Function Transform and Matrix-Valued Orthogonal Polynomials [PDF]
Constructive Approximation, 2013 The spectral decomposition for an explicit second-order differential operator $T$ is determined. The spectrum consists of a continuous part with multiplicity two, a continuous part with multiplicity one, and a finite discrete part with multiplicity one.
Groenevelt, W., Koelink, E.
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Matrix valued orthogonal polynomials satisfying differential equations [PDF]
, 2007 The theory of matrix valued orthogonal polynomials goes back to the fundamental works of M. G. Krein. If one is considering possible applications of these polynomials, it is natural to concentrate on those cases where some extra property holds.
Domínguez de la Iglesia, Manuel
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Asymptotics of matrix valued orthogonal polynomials on [−1,1] [PDF]
Advances in Mathematics, 2023 We analyze the large degree asymptotic behavior of matrix valued orthogonal polynomials (MVOPs), with a weight that consists of a Jacobi scalar factor and a matrix part. Using the Riemann-Hilbert formulation for MVOPs and the Deift-Zhou method of steepest descent, we obtain asymptotic expansions for the MVOPs as the degree tends to infinity, in ...
Deano, Alfredo +2 more
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Matrix polynomials orthogonal with respect to a non-symmetric matrix of measures [PDF]
Opuscula Mathematica, 2016 The paper focuses on matrix-valued polynomials satisfying a three-term recurrence relation with constant matrix coefficients. It is shown that they form an orthogonal system with respect to a matrix of measures, not necessarily symmetric. Moreover, it is
Marcin J. Zygmunt
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A note on the invariant distribution of a quasi-birth-and-death process [PDF]
, 2010 The aim of this paper is to give an explicit formula of the invariant distribution of a quasi-birth-and-death process in terms of the block entries of the transition probability matrix using a matrix-valued orthogonal polynomials approach.
Dette H +12 more
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Random matrices with equispaced external source [PDF]
, 2013 We study Hermitian random matrix models with an external source matrix which has equispaced eigenvalues, and with an external field such that the limiting mean density of eigenvalues is supported on a single interval as the dimension tends to infinity ...
Claeys, Tom, Wang, Dong
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