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• W330849295 startingPage "517" @default.
• W330849295 abstract "Baryshnikov [4] and Gravner, Tracy & Widom [15] have shown that the largest eigenvalue of a random matrix of the G.U.E. of order d has the same distribution as where is a d-dimensional Brownian motion. We provide a generalization of this formula to all the eigenvalues and give a geometric interpretation. For any Weyl chamber a+ of an Euclidean finite-dimensional space a, we define a natural continuous path transformation T which associates to a path w in a a path Tw in ¯a+. This transformation occurs in the description of the asymptotic behaviour of some deterministic dynamical systems on the symmetric space G/K where G is the complex group with chamber a+. When and if W is the Euclidean Brownian motion on a then T W is the process of the eigenvalues of the Dyson Brownian motion on the set of Hermitian matrices and (T W)(1) is distributed as the eigenvalues of the G.U.E." @default.
• W330849295 created "2016-06-24" @default.
• W330849295 creator A5036431515 @default.
• W330849295 creator A5080705821 @default.
• W330849295 date "2002-12-01" @default.
• W330849295 modified "2023-10-18" @default.
• W330849295 title "Paths in Weyl chambers and random matrices" @default.
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• W330849295 doi "https://doi.org/10.1007/s004400200221" @default.
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