Discrete Orthogonal Polynomial Ensembles and the Plancherel Measure
نویسندگان
چکیده
منابع مشابه
Discrete orthogonal polynomial ensembles and the Plancherel measure
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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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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We show that the function h(x) = ∏ i<j(xj − xi) is harmonic for any random walk in Rk with exchangeable increments, provided the required moments exist. For the subclass of random walks which can only exit the Weyl chamber W = {x : x1 < x2 < · · · < xk} onto a point where h vanishes, we define the corresponding Doob h-transform. For certain special cases, we show that the marginal distribution ...
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ژورنال
عنوان ژورنال: The Annals of Mathematics
سال: 2001
ISSN: 0003-486X
DOI: 10.2307/2661375