An asymptotic link between LUE and GUE and its spectral interpretation

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We use a matrix central-limit theorem which makes the Gaussian Unitary Ensemble appear as a limit of the Laguerre Unitary Ensemble together with an observation due to Johansson in order to derive new representations for the eigenvalues of GUE. For instance, it is possible to recover the celebrated equality in distribution between the maximal eigenvalue of GUE and a last-passage time in some directed brownian percolation. Similar identities for the other eigenvalues of GUE also appear.
15 pages, 1 figure

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Probability

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http://salesiana.dossiersoluciones.com/handle/123456789/63809

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0204175
 http://arxiv.org/abs/math/0204175

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arXiv