Orthogonal polynomial ensembles in probability theory
نویسندگان
چکیده
منابع مشابه
Orthogonal polynomial ensembles in probability theory
We survey a number of models from physics, statistical mechanics, probability theory and combinatorics, which are each described in terms of an orthogonal polynomial ensemble. The most prominent example is apparently the Hermite ensemble, the eigenvalue distribution of the Gaussian Unitary Ensemble (GUE), and other well-known ensembles known in random matrix theory like the Laguerre ensemble fo...
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Multiple orthogonal polynomials are traditionally studied because of their connections to number theory and approximation theory. In recent years they were found to be connected to certain models in random matrix theory. In this paper we introduce the notion of a multiple orthogonal polynomial ensemble (MOP ensemble) and derive some of their basic properties. It is shown that Angelesco and Niki...
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We consider discrete orthogonal polynomial ensembles which are discrete analogues of the orthogonal polynomial ensembles in random matrix theory. These ensembles occur in certain problems in combinatorial probability and can be thought of as probability measures on partitions. The Meixner ensemble is related to a two-dimensional directed growth model, and the Charlier ensemble is related to the...
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Multiple orthogonal polynomials (MOP) are a non-definite version of matrix orthogonal polynomials. They are described by a Riemann-Hilbert matrix Y consisting of four blocks Y1,1, Y1,2, Y2,1 and Y2,2. In this paper, we show that detY1,1 (detY2,2) equals the average characteristic polynomial (average inverse characteristic polynomial, respectively) over the probabilistic ensemble that is associa...
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The study of the asymptotic properties of the largest eigenvalues of random matrices gave recently rise to a number of important developments. To illustrate one typical example in the context of sample covariance matrices, let G = G be an N ×N random matrix whose entries are independent standard complex Gaussian random variables, and denote by X = X = GG∗ the so-called Wishart matrix (with cova...
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ژورنال
عنوان ژورنال: Probability Surveys
سال: 2005
ISSN: 1549-5787
DOI: 10.1214/154957805100000177